You can find ALL Preprints here.

• M.E. Akramov, J.R. Yusupov, M. Ehrhardt, H. Susanto and D.U. Matrasulov, Transparent PT-symmetric nonlinear networks, Preprint 24/10, August 2024.
• M. Ehrhardt and C. Zheng, Absorbing Boundary Conditions for Variable Potential Schrödinger Equations via Titchmarsh-Weyl Theory, Preprint 24/09, August 2024.
• A. Zinihi, M.R. Sidi Ammi, M. Ehrhardt and A. Bachir, Dynamical Analysis of a Cocaine-Heroin Epidemiological Model with Spatial Distributions, Preprint 24/08, May 2024.
• A. Zinihi, M.R. Sidi Ammi and M. Ehrhardt, Dynamical Behavior of a Stochastic Epidemiological Model: Stationary Distribution and Extinction of a SIRS Model with Stochastic Perturbations, Preprint 24/07, April 2024.
• L. Di Persio, M. Ehrhardt and S. Rizzotto, Integrating Port-Hamiltonian Systems with Neural Networks: From Deterministic to Stochastic Frameworks, Preprint 24/06, April 2024.
• A. Zinihi, M.R. Sidi Ammi and M. Ehrhardt, Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative, Preprint 24/04, March 2024.
• Manh Tuan Hoang and M. Ehrhardt, Differential equation models for infectious diseases: Mathematical modeling, qualitative analysis, numerical methods and applications, Preprint 24/02, February 2024.
• J.R. Yusupov, M. Ehrhardt, Kh.Sh. Matyokubov and D.U. Matrasulov, Driven transparent quantum graphs, Preprint 23/19, November 2023.
• T. Kossaczká, M. Ehrhardt and M. Günther, Deep finite difference method for solving Asian option pricing problems, Preprint 23/17, October 2023.
• H. Fatoorehchi, M. Noorimohammad, A. Houshmand and M. Ehrhardt, A Compressiblity Factor-Explicit Equation of State Based on the Carnahan-Starling-de Santis Equation and the Adomian Decomposition Method, April 2023.
• H. Fatoorehchi, R. Zarghami and M. Ehrhardt, A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control, Preprint 23/01, January 2023.
• A. Clevenhaus, M. Ehrhardt and M. Günther, A parallel Sparse Grid Combination Technique using the Parareal Algorithm, Preprint 21/18, June 2021.
• L. Di Persio, M. Ehrhardt and B. Verzé, Solar Energy Forecasting: from classical statistical approaches to innovative machine learning based models, Preprint 18/19, December 2018.
• I. Kossaczký, M. Ehrhardt and M. Günther, A new convergent explicit Tree-Grid Method for HJB equations in one space dimension, Preprint 17/06, June 2017.
• Z. Bučková, P. Pólvora, M. Ehrhardt and M. Günther, Implementation of alternating direction explicit methods for higher dimensional Black-Scholes equations, Preprint 16/20, October 2016.
• I. Kossaczký, M. Ehrhardt and M. Günther, Piecewise fixed policy timestepping schemes for Hamilton-Jacobi-Bellman equations, Preprint 16/13, July 2016.
• T. Deutsch and M. Ehrhardt, Mathematical Modelling of Radicalization Processes: the Example of Right-wing Extremism in Germany, Preprint 15/20, April 2015.
• C. Hendricks, M. Ehrhardt and M. Günther, High-Order-Compact ADI schemes for diffusion equations with mixed derivatives in the combination technique, Preprint 15/14, February 2015.
• L. Teng, M. Ehrhardt and M. Günther, Numerical Simulation of the Heston model with Stochastic Correlation, Preprint 15/01, January 2015.
• C. Hendricks, M. Ehrhardt and M. Günther, High Order Tensor Product Interpolation in the Combination Technique, Preprint 14/25, August 2014.
• M. Ehrhardt and R. Valkov, Numerical analysis of nonlinear European option pricing problem in illiquid markets, Preprint 14/23, August 2014.
• M. Ehrhardt and R. Valkov, A stable explicit finite difference scheme for a nonlinear European option pricing problem, Preprint 13/23, October 2013.
• C. Hendricks and M. Ehrhardt, Clean Spread Options in the German Electricity Market, Preprint 13/09, July 2013.
• T. Amro, A. Arnold and M. Ehrhardt, Optimized Far Field Boundary Conditions for Hyperbolic Systems, Preprint 12/02, January 2012.
• X. Antoine, C. Besse, M. Ehrhardt and P. Klein, Modeling boundary conditions for solving stationary Schrödinger equations, Preprint 10/04, February 2010.
• M. Ehrhardt, J. Fuhrmann and A. Linke, A model of an electrochemical flow cell with porous layer, Preprint 09/04, October 2009.

1. L. Teng, M. Ehrhardt and M. Günther, Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance, World Scientific, scheduled 2024.
2. M. Ehrhardt and M. Günther, Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft, Springer, scheduled 2024.
3. M. Ehrhardt, M. Günther and W. Schilders, Mimetic Numerical methods, Structure Preservation and port-Hamiltonian Systems, Springer, scheduled 2024.
4. M. Ehrhardt and M. Günther (eds.), Progress in Industrial Mathematics at ECMI 2021, The European Consortium for Mathematics in Industry Vol. 39, Springer, November 2022. ISBN 978-3-031-11817-3.
5. T. Jax, A. Bartel, M. Ehrhardt, M. Günther and G. Steinebach, (eds.), Rosenbrock-Wanner-Type Methods: Theory and Applications, Springer, 2021. DOI: 10.1007/978-3-030-76810-2
6. M. Ehrhardt, M. Günther and J. ter Maten, (eds.), Novel Methods in Computational Finance, Vol. 25 of the Springer series Mathematics in Industry of The European Consortium for Mathematics in Industry (ECMI), September 2017.
7. M. Ehrhardt (ed.), Mathematical Modelling and Numerical Simulation of Oil Pollution Problems, Vol. 2 of the Springer series The Reacting Atmosphere, March 2015.
8. M. Ehrhardt and Th. Koprucki (eds.), Multi-Band Effective Mass Approximations - Advanced Mathematical Models and Numerical Techniques, LNCSE, Vol. 94, Springer Verlag, Heidelberg, 2014.
9. M. Ehrhardt (ed.), Novel Trends in Lattice-Boltzmann Methods - Reactive Flow, Physicochemical Transport and Fluid-Structure Interaction, Progress in Computational Physics, Vol. 3, Bentham Science Publishers Ltd., 2013.
10. M. Ehrhardt (ed.), Coupled Fluid Flow in Energy, Biology and Environmental Research, Progress in Computational Physics, Vol. 2, Bentham Science Publishers Ltd., 2012.
11. M. Ehrhardt (ed.), Wave Propagation in Periodic Media - Analysis, Numerical Techniques and practical Applications, Progress in Computational Physics, Vol. 1, Bentham Science Publishers Ltd., 2010.
12. M. Ehrhardt (ed.), Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2008. ISBN: 978-1-60456-931-5
13. M. Ehrhardt, Discrete Artificial Boundary Conditions, Verlag dissertation.de, Berlin, 2001.

1. C. Ceci, F. Cesarone, M. Ehrhardt, G. Orlando, J. Puerto, and F. Tardella (eds.), Advances in Risk and Portfolio Management, Wiley, 2023.
2. M. Ehrhardt, M. Grossinho and D. Sevcovic (eds.), Recent Advances on Nonlinear Models in Mathematical Finance II, Special Issue of Mathematics Journal, 2023.
3. S. Pereselkov, M. Ehrhardt, and P. Petrov (eds.), Underwater Acoustics and Digital Signal Processing, Special Issue of Journal of Marine Science and Engineering, 2023.
4. M. Ehrhardt, M. do Rosário Grossinho, C.-H. Lai, K. Oosterlee, D. Sevcovic, and C. Vázquez, (eds.), ICCF 2022 - Novel Methods in Computational Finance, Special Issue of International Journal of Computer Mathematics of selected papers from these fields in Computational Finance, presented at ICCF 2022 - 4th International Conference on Computational Finance, June 6-10, 2022, Wuppertal, Germany.
5. M. Ehrhardt and C. Reisinger (eds.), Selected contributions from 4th International Conference on Computational Finance 2022, Special Issue of Journal of Computational Finance, Risk.net, scheduled 2023.
6. M. Ehrhardt and M. Günther (eds.), Selected topics from 21st ECMI Conference on Industrial and Applied Mathematics, Special Issue of Journal of Mathematics in Industry, Springer, scheduled 2023.
7. M. Ehrhardt, M. Grossinho and D. Sevcovic (eds.), Recent Advances on Nonlinear Models in Mathematical Finance, Special Issue of Mathematics Journal, 2021.
8. A. Micheletti, A. Araújo, N. Budko, A. Carpio and M. Ehrhardt (eds.), Mathematical models of the spread and consequences of the SARS-CoV-2 pandemics. Effects on health, society, industry, economics and technology, Special Issue of Journal of Mathematics in Industry, Springer, September 2021.
9. B. Chaudhury, M. Ehrhardt and V. Bokil, Finite Difference Methods: Recent Developments and Applications in Computational Science, Special Issue of Journal of Computational Science, Elsevier, 2019.
10. M. Coulon, M. Ehrhardt, M. do Rosário Grossinho, K. In 't Hout, C. Oosterlee, A. Shiryaev, N. Touzi and C. Vázquez, (eds.), ICCF 2017 - Novel Methods in Computational Finance, Special Issue of Applied Mathematical Finance of selected papers from these fields in Computational Finance, presented at ICCF 2017 - 2nd International Conference on Computational Finance, September 4-8, 2017, Lisbon, Portugal.
11. C.-H. Lai, M. do Rosário Grossinho, M. Ehrhardt, M. Guerra, J. Janela, D. Sevcovic and C. Vázquez, (eds.), ICCF 2017 - Novel Methods in Computational Finance, Special Issue of International Journal of Computer Mathematics of selected papers from these fields in Computational Finance, presented at ICCF 2017 - 2nd International Conference on Computational Finance, September 4-8, 2017, Lisbon, Portugal.
12. M. Ehrhardt, M. do Rosário Grossinho, D. Sevcovic and A. Shriyaev, (eds.), Stochastic and Computational Finance - From Academia to Industry, Special Issue of International Journal of Computer Mathematics of selected papers from these fields, presented at the International Conference SCF 2015 - Stochastic and Computational Finance - From Academia to Industry, July 5-10, 2015, Lisbon, Portugal.
13. M. Ehrhardt, L. Vulkov and S. Wang (eds.), Novel Methods in Computational Finance, Special Issue of Computational Methods in Applied Mathematics of selected papers from these fields in Computational Mathematics and its applications, presented at the the Sixth Conference Finite Difference Methods: Theory and Applications, June 18-23, 2014, Lozenetz, Bulgaria.
14. R. Company, M. Ehrhardt and L. Jodar Sánchez (eds.), Novel Methods in Computational Finance, Special Issue of International Journal of Computer Mathematics of selected papers from these fields in Computational Mathematics and its applications, presented at the International Conference on Mathematical Modelling in Engineering & Human Behaviour 2013, September 4-6, 2013, Instituto Universitario de Matemática Multidisciplinar, Polytechnic City of Innovation in Valencia, Spain.
15. M. Ehrhardt, L. Jodar Sánchez and R.J. Villanueva (eds.), Numerical Methods and Mathematical Modelling in Biology, Medicine and Social Sciences, Special Issue of International Journal of Computer Mathematics of selected papers from these fields in Computational Mathematics and its applications, presented at the International Conference on Mathematical Modelling in Engineering & Human Behaviour 2012, September 4-7, 2012, Instituto Universitario de Matemática Multidisciplinar, Polytechnic City of Innovation in Valencia, Spain.
16. M. Ehrhardt, L. Jodar Sánchez and R.J. Villanueva (eds.), Advanced Computational Engineering, Special Issue of International Journal of Computer Mathematics of selected papers from these fields in Computational Mathematics and its applications, presented at the International Conference on Mathematical Modelling in Engineering & Human Behaviour 2012, September 4-7, 2012, Instituto Universitario de Matemática Multidisciplinar, Polytechnic City of Innovation in Valencia, Spain.

1. G. Morais Rodrigues Costa, M. Lobosco, M. Ehrhardt and R.F. Reis, Mathematical Analysis and a Nonstandard Scheme for a Model of the Immune Response against COVID-19, in: A. Gumel (ed.), Mathematical and Computational Modeling of Phenomena Arising in Population Biology and Nonlinear Oscillations, Contemporary Mathematics, vol. 793, Amer. Math. Soc., Providence, RI, 2024, pp. 251-270. DOI: 10.1090/conm/793/15881.
2. J. Backhaus, M. Bolten, O.T. Doganay, M. Ehrhardt, et al., GivEn - Shape Optimization for Gas Turbines in Volatile Energy Networks, in: S. Göttlich, M. Herty and A. Milde (eds.), Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, Mathematics in Industry, vol. 34. Springer, Cham, 2021, pp. 71-106. DOI: 10.1007/978-3-030-62732-4_4.
3. L. Teng, M. Ehrhardt and M. Günther, Modelling and Calibration of Stochastic Correlation in Finance, Chapter in: M. Ehrhardt, M. Günther and J. ter Maten, (eds.), Novel Methods in Computational Finance, Springer, 2017, pp. 83-105.
4. Z. Bučková, M. Ehrhardt, M. Günther and P. Pólvora, Alternating Direction Explicit Methods for Linear, Nonlinear and Multi-dimensional Black-Scholes Models, Chapter in: M. Ehrhardt, M. Günther and J. ter Maten, (eds.), Novel Methods in Computational Finance, Springer, 2017, pp. 333-371.
5. C. Hendricks, C. Heuer, M. Ehrhardt and M. Günther, High-Order-Compact ADI schemes for pricing basket options in the combination technique, Chapter in: M. Ehrhardt, M. Günther and J. ter Maten, (eds.), Novel Methods in Computational Finance, Springer, 2017, pp. 399-405.
6. J.P. Silva, E.J.W. ter Maten, M. Günther and M. Ehrhardt Proper Orthogonal Decomposition in Option Pricing, Chapter in: M. Ehrhardt, M. Günther and J. ter Maten, (eds.), Novel Methods in Computational Finance, Springer, 2017, pp. 441-452.
7. C. Heuer, P. Pólvora, J. Silva, M. Ehrhardt, M. Günther and E.J.W. ter Maten, The STRIKE Computational Finance Toolbox, Chapter in: M. Ehrhardt, M. Günther and J. ter Maten, (eds.), Novel Methods in Computational Finance, Springer, 2017, pp. 561-601.
8. L. Teng, M. Ehrhardt and M. Günther, The Dynamic Correlation Model and Its Application to the Heston Model, Chapter in: K. Glau et al: Innovations in Derivatives Markets, Springer, 2016.
9. L. Teng, C. van Emmerich, M. Ehrhardt and M. Günther, Modelling Stochastic Correlation with modified Ornstein-Uhlenbeck process, In ECMI book subseries of Mathematics in Industry, ISSN: 1612-3956, Springer Heidelberg, 2015.
10. M. Ehrhardt, M. Peco, A.-C. Tarazona, R.-J. Villanueva and J. Villanueva-Oller, Popular Support to Terrorist Organizations: A Short-Term Prediction based on a Dynamic Model applied to a Real Case, Chapter 16 in: J.C. Cortés, L. Jodar Sánchez and R.J. Villanueva (eds.), Mathematical Modeling in Engineering & Social Sciences, Nova Science, 2014, pp. 169-176, ISBN: 978-1-63117-335-6.
11. M. Ehrhardt, Nonstandard Finite Difference Schemes for the Black-Scholes Equation, Chapter 11 in: A. Gumel (ed.), Mathematics of Continuous and Discrete Dynamical Systems, AMS (Contemporary Mathematics), Vol. 618, 2014, pp. 217-228.
12. A. Zisowsky, A. Arnold, M. Ehrhardt and Th. Koprucki, Transient Simulation of kp-Schrödinger Systems using Discrete Transparent Boundary Conditions, Chapter 5 in: M. Ehrhardt and Th.  Koprucki (eds.), Multi-Band Effective Mass Approximations - Advanced Mathematical Models and Numerical Techniques, Springer Verlag, Heidelberg, 2014, pp. 247-272.
13. D. Klindworth, M. Ehrhardt and Th.  Koprucki, Discrete Transparent Boundary Conditions for Multiband Effective Mass Approximations, Chapter 6 in: M. Ehrhardt and Th.  Koprucki (eds.), Multi-Band Effective Mass Approximations - Advanced Mathematical Models and Numerical Techniques, Springer Verlag, Heidelberg, 2014, pp. 273-318.
14. M. Ehrhardt, M. Günther and B. Jacob, Modelling and Numerical Simulation, Chapter 4 in: R. Koppmann (ed.), Atmospheric Research From Different Perspectives, The Reacting Atmosphere 1, Springer Verlag, 2014, pp. 27-34. DOI: 10.1007/978-3-319-06495-6_4
15. D. Heubes, A. Bartel and M. Ehrhardt, An Introduction to Lattice-Boltzmann Methods, Chapter 1 in: M. Ehrhardt (ed.), Novel Trends in Lattice-Boltzmann Methods - Reactive Flow, Physicochemical Transport and Fluid-Structure Interaction, Progress in Computational Physics, Vol. 3, Bentham Science Publishers Ltd., 2013.
16. M. Ehrhardt, An Introduction to Fluid-Porous Interface Coupling, Chapter 1 in: M. Ehrhardt (ed.), Coupled Fluid Flow in Energy, Biology and Environmental Research, Progress in Computational Physics, Vol. 2, Bentham Science Publishers Ltd., May 2012.
17. M. Beitz and M. Ehrhardt, A New Method for Stress Testing on Investment Products, Chapter 10 in: Michael C.S. Wong (Ed.), The Risk of Investment Products: From Product Innovation to Risk Compliance, World Scientific Publishing, 2011, pp. 223-238.
18. M. Ehrhardt and C. Zheng, Fast numerical methods for the simulation of waves in periodic structures, Chapter 6 in: M. Ehrhardt (ed.), Wave Propagation in Periodic Media - Analysis, Numerical Techniques and practical Applications, Progress in Computational Physics, Vol. 1, Bentham Science Publishers Ltd., June 2010, pp. 135-166.
19. Quang A Dang, M. Ehrhardt, Gia Lich Tran and Duc Le, On the numerical solution of some problems of environmental pollution, Chapter 6 in: P. Robinson and R.  Gallo (ed.), Environmental Chemistry Research Progress, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2009, pp. 199-228.
20. A. Arnold, M. Ehrhardt and M. Schulte, Numerical Simulation of Quantum Waveguides, Chapter 4 in: K. Watanabe (ed.), VLSI and Computer Architecture, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2009, pp. 115-137.
21. M. Ehrhardt, Nonlinear Models in Option Pricing - an Introduction, Preface in: M. Ehrhardt (ed.), Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2008, pp. 1-19.
22. J. Ankudinova and M. Ehrhardt, Fixed domain transformations and split-step finite difference schemes for Nonlinear Black-Scholes equations for American Options, Chapter 8 in: M. Ehrhardt (ed.), Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2008, pp. 243-273.
23. Quang A Dang, M. Ehrhardt, Gia Lich Tran and Duc Le, On the numerical solution of some problems of environmental pollution, Chapter 8 in: C.B. Bodine (ed.), Air Pollution Research Advances, Nova Science Publishers, Inc., Hauppauge, NY 11788, 2007, pp. 171-200.
24. M. Ehrhardt, Finite Difference Schemes on unbounded Domains, Chapter 8 in: R.E. Mickens (ed.), Applications of Nonstandard Finite Difference Schemes, Volume 2, World Scientific, 2005, pp. 343-384.

1. M. Ehrhardt and A. Tordeux, Stability of heterogeneous linear and nonlinear car-following models, accepted: Franklin Open, 2024.
2. A. Zinihi, M.R. Sidi Ammi and M. Ehrhardt, Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with Φ_p Operator and Mittag-Leffler Kernel, accepted: Advances in Applied Mathematics and Mechanics, 2024. DOI: 10.4208/aamm.OA-2024-0134.
3. Z. Zheng, G. Pang, M. Ehrhardt and B. Liu, A fast second-order absorbing boundary condition for the linearized Benjamin-Bona-Mahony equation, Numerical Algorithms (2024). DOI: 10.1007/s11075-024-01864-2
4. J. Ackermann, M. Ehrhardt, T. Kruse and A. Tordeux, Stabilisation of Stochastic Single-File Dynamics using Port-Hamiltonian Systems, IFAC-PapersOnLine, Volume 58, Issue 17, 2024, Pages 145-150. DOI: 10.1016/j.ifacol.2024.10.128.
5. H. Fatoorehchi and M. Ehrhardt, Advanced stability assessment for control systems: Gelfand's method with iterated shanks transformation, Indian Chemical Engineer (2024), 1-12. DOI: 10.1080/00194506.2024.2357786.
6. S. Pereselkov, V. Kuz'kin, M. Ehrhardt, Y. Matvienko, I. Kaznacheev and P. Rybyanets, The Formation of 2D-Holograms of Noise Source and Bearing Estimation by a Vector Scalar Receiver in the High-Frequency Band, Journal of Marine Science and Engineering, Section Physical Oceanography, 2024, 12(5), 704. DOI: 10.3390/jmse12050704.
7. T. Kossaczká, A. Jagtap and M. Ehrhardt, Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators, Physics of Fluids 36 (2024), 036603. DOI: 10.1063/5.0199322.
8. A. Clevenhaus, C. Totzeck and M. Ehrhardt, A gradient based calibration method for the Heston model, International Journal of Computer Mathematics (2024), 1-19. DOI: 10.1080/00207160.2024.2353189.
9. P.S. Petrov, M. Ehrhardt and S.B. Kozitskiy, On a generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide, Journal of Sound and Vibration, Volume 577 (2024), 118304. DOI: 10.1016/j.jsv.2024.118304.
10. M. Ehrhardt, T. Kruse and A. Tordeux, The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension, ESAIM: Mathematical Modelling and Numerical Analysis Volume 58 (2024), 515-544. DOI: 10.1051/m2an/2024004.
    Erratum: in the middle of Remark 2.1. it should read: (i.e., p_n (t) = (p_n+1(t) + p_n-1(t))/2)
11. Manh Tuan Hoang and M. Ehrhardt, A second-order nonstandard finite difference method for a general Rosenzweig-MacArthur predator-prey model, Journal of Computational and Applied Mathematics, Volume 444 (2024), 115752. DOI: 10.1016/j.cam.2024.115752.
12. M.H. Maamar, M. Ehrhardt and L. Tabharit, A Nonstandard Finite Difference Scheme for a Time-Fractional Model of Zika Virus Transmission, Mathematical Biosciences and Engineering, Volume 21, Issue 1 (2024), 924-962. (Special Issue: Mathematical Models and Computational Tools of Infectious Diseases) DOI: 10.3934/mbe.2024039.
13. Manh Tuan Hoang and M. Ehrhardt, A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model, Journal of Difference Equations and Applications 30(4) (2024), 409-434. DOI: 10.1080/10236198.2023.2291151.
14. H. Fatoorehchi and M. Ehrhardt, A novel technique for stability analysis of linear time-invariant and nonlinear continuous- time control systems based on Markov parameters and Hankel matrices, Transactions of the Institute of Measurement and Control 46(10) (2024), 1910-1923. DOI: 10.1177/01423312231216209.
15. Manh Tuan Hoang and M. Ehrhardt, A general class of second-order L-stable explicit numerical methods for stiff problems, Applied Mathematics Letters 149 (2024) 108897. DOI: 10.1016/j.aml.2023.108897.
16. S. Pereselkov, V. Kuz'kin, M. Ehrhardt, S. Tkachenko, P. Rybyanets and N. Ladykin, 3D Modeling of Sound Field Hologram of Moving Source in Presence of Internal Waves Causing Horizontal Refraction, Journal of Marine Science and Engineering, Section Physical Oceanography, 2023, 11(10), 1922. DOI: 10.3390/jmse11101922.
17. T. Kossaczká, M. Ehrhardt and M. Günther, Deep FDM: Enhanced finite difference methods by deep learning, Franklin Open, Volume 4, 2023, 100039. DOI: 10.1016/j.fraope.2023.100039.
18. M. Muniz, M. Ehrhardt, M. Günther and R. Winkler, Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds, Applied Numerical Mathematics, Volume 193, November 2023, 196-203. DOI: 10.1016/j.apnum.2023.07.024.
19. J.R. Yusupov, Kh.Sh. Matyokubov, M. Ehrhardt and D.U. Matrasulov, Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks, Physics Letters A, Volume 479 (2023), 128928. DOI: 10.1016/j.physleta.2023.128928.
20. F. Heldmann, S. Berkhahn, M. Ehrhardt and K. Klamroth, PINN Training using Biobjective Optimization: The Trade-off between Data Loss and Residual Loss, Journal of Computational Physics, Volume 488 (2023), 112211. DOI: 10.1016/j.jcp.2023.112211.
21. H. Fatoorehchi and M. Ehrhardt, A combined method for stability analysis of linear time invariant and nonlinear continuous-time control systems based on the Hermite-Fujiwara matrix and Cholesky decomposition, Canadian Journal of Chemical Engineering, Volume 101 (2023), 7043-7052. DOI: 10.1002/cjce.24962.
22. A. Poggi, L. Di Persio and M. Ehrhardt, Electricity Price Forecasting via Statistical and Deep Learning Approaches: the German case, AppliedMath 2023, 3(2), 316-342. DOI: 0.3390/appliedmath3020018.
23. S. Pereselkov, V. Kuz'kin, M. Ehrhardt, S. Tkachenko, P. Rybyanets and N. Ladykin, Use of Interference Patterns to Control Sound Field Focusing in Shallow Water, Journal of Marine Science and Engineering 2023, 11(3), 559. DOI: 10.3390/jmse11030559.
24. M.E. Akramov, J.R. Yusupov, M. Ehrhardt, H. Susanto and D.U. Matrasulov, Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons, Physics Letters A, Volume 459, January 2023, 128611. DOI: 10.1016/j.physleta.2022.128611.
25. J. Jäschke, N. Skrepek and M. Ehrhardt, Mixed-Dimensional Geometric Coupling of Port-Hamiltonian Systems, Applied Mathematics Letters, Volume 137, March 2023, 108508. DOI: 10.1016/j.aml.2022.108508.
26. M. Ehrhardt, S. Pereselkov, V. Kuz'kin, I. Kaznacheev and P. Rybyanets, Experimental Observation and Theoretical Analysis of the Low-frequency Source Interferogram and Hologram in Shallow Water, Journal of Sound and Vibration, Volume 544, February 2023, 117388. DOI: 10.1016/j.jsv.2022.117388.
27. J. Jäschke, M. Ehrhardt, M. Günther and B. Jacob, A Two-Dimensional Port-Hamiltonian Model for Coupled Heat Transfer, Mathematics 2022, 10(24), 4635; (Special Issue "Completely Integrable Equations: Algebraic Aspects and Applications") DOI: 10.3390/math10244635.
28. S. Berkhahn and M. Ehrhardt, A Physics-Informed Neural Network to Model COVID-19 Infection and Hospitalization Scenarios, Advances in Continuous and Discrete Models: Theory and Applications 2022, 61 (2022). DOI: 10.1186/s13662-022-03733-5.
29. L. Agasthya, A. Bartel, L. Biferale, M. Ehrhardt and F. Toschi, Large-scale convective flow sustained by thermally active Lagrangian tracers, Journal of Fluid Mechanics 953 (2022), A5. DOI: 10.1017/jfm.2022.892.
30. J. Jäschke, M. Ehrhardt, M. Günther and B. Jacob, A Port-Hamiltonian Formulation of Coupled Heat Transfer, Mathematical and Computer Modelling of Dynamical Systems, Volume 28, Issue 1 (2022), 78-94. DOI: 10.1080/13873954.2022.2038637.
31. T. Kossaczká, M. Ehrhardt and M. Günther, A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations, Physics of Fluids, Vol. 34, Issue 2, (2022), 026604. DOI: 10.1063/5.0078397.
32. M. Muniz, M. Ehrhardt, M. Günther and R. Winkler, Higher Strong Order Methods for Itô SDEs on Matrix Lie Groups, BIT Numerical Mathematics, 62,(2022), 1095-1119. DOI: 10.1007/s10543-021-00905-9.
33. H. Fatoorehchi and M. Ehrhardt, Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells, Journal of Energy Storage, Vol. 45, (January 2022), 103746. DOI: 10.1016/j.est.2021.103746.
34. S. Treibert, H. Brunner and M. Ehrhardt, A Nonstandard Finite Difference Scheme for the SVICDR model to predict COVID-19 dynamics, Mathematical Biosciences and Engineering 19(2) (2022), 1213-1238. DOI: 10.3934/mbe.2022056.
35. K.K. Sabirov, J.R. Yusupov, M. Ehrhardt and D.U. Matrasulov, Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line, Physics Letters A, Vol. 423 (2022), 127822. DOI: 10.1016/j.physleta.2021.127822.
36. P.S. Petrov, M. Ehrhardt and M.Yu. Trofimov, On the decomposition of the fundamental solution of the Helmholtz equation via solutions of iterative parabolic equations, Asymptotic Analysis, vol. 126, no. 3-4 (2022), 215-228. DOI: 10.3233/ASY-211679
37. M. Muniz, M. Ehrhardt, M. Günther and R. Winkler, Stochastic Runge-Kutta-Munthe-Kaas methods in the modelling of perturbed rigid bodies, Advances in Applied Mathematics and Mechanics, Vol. 14, No. 2, (2022), 528-538. DOI: 10.4208/aamm.OA-2021-0176
38. T. Kossaczká, M. Ehrhardt and M. Günther, Enhanced fifth order WENO Shock-Capturing Schemes with Deep Learning, Results in Applied Mathematics (2021), 100201. DOI: 10.1016/j.rinam.2021.100201.
39. K.K. Sabirov, J.R. Yusupov, M.M. Aripov, M. Ehrhardt and D.U. Matrasulov, Reflectionless propagation of Manakov solitons on a line: A model based on the concept of transparent boundary conditions, Physical Review E, Vol. 103, No. 4 (2021), 043305. DOI: 10.1103/PhysRevE.103.043305
40. A. Clevenhaus, M. Ehrhardt and M. Günther, An ADI Sparse Grid method for pricing efficiently American Options under the Heston model, Advances in Applied Mathematics and Mechanics, Volume 13 (2021), 1384-1397. DOI: 10.4208/aamm.OA-2020-0317
41. E. Viviani, L. Di Persio and M. Ehrhardt, Energy markets forecasting. From Inferential Statistics to Machine Learning: the German case, Energies 2021, 14(2), 364; DOI: 10.3390/en14020364
42. M. Muniz, M. Ehrhardt and M. Günther, Approximating correlation matrices using stochastic Lie group methods, Mathematics 2021, 9(1), 94. DOI: 10.3390/math9010094
43. N. Umeorah, P. Mashele and M. Ehrhardt, Pricing Basket Default Swaps Using Quasi-Analytic Techniques, Decisions in Economics and Finance 1/2021, Springer. DOI: 10.1007/s10203-020-00310-x
44. P. Csomós, M. Ehrhardt and B. Farkas, Operator splitting for abstract Cauchy problems with dynamical boundary conditions, Operators and Matrices, Volume 15, Number 3, September 2021, 903-935. DOI: 10.7153/oam-2021-15-60.
45. P.S. Petrov, M. Ehrhardt, A.G. Tyshchenko and P.N. Petrov, Wide-angle mode parabolic equations for the problems of underwater acoustics and their numerical solution on unbounded domains, Journal of Sound and Vibration, Volume 484 (2020), 115526. DOI: 10.1016/j.jsv.2020.115526
46. A. Clevenhaus, M. Ehrhardt, M. Günther and D. Sevcovic, Pricing American Options with a Non-constant Penalty Parameter, J. Risk Financial Manag. 13(6) (2020), 124. DOI: 10.3390/jrfm13060124
47. N. Umeorah, M. Ehrhardt and P. Mashele, Valuation of Basket Credit Default Swaps Under Stochastic Default Intensity Models, Adv. Appl. Math. Mech., Volume 12 (2020), 1301-1326. DOI: 10.4208/aamm.OA-2019-0141.
48. J.R. Yusupov, K.K. Sabirov, Q.U. Asadov, M. Ehrhardt and D.U. Matrasulov, Dirac Particles in Transparent Quantum Graphs: Tunable transport of relativistic quasiparticles in branched structures, Physical Review E, Volume 101, Number 6 (June 2020), 062208. DOI: 10.1103/PhysRevE.101.062208.
49. N. Umeorah, P. Mashele and M. Ehrhardt, Elliptical and Archimedean copula models: an application to the price estimation of portfolio credit derivatives, Journal of Credit Risk, Technical Report 2020.
50. L. Teng, X. Wu, M. Günther and M. Ehrhardt, A new methodology to create valid time-dependent correlation matrices via isospectral flows, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), Volume 54, Number 2, (March-April 2020), 361-371. DOI: 10.1051/m2an/2019064.
51. M. Ehrhardt, J. Gašper and S. Kilianová, SIR-based Mathematical Modeling of Infectious Diseases with Vaccination and Waning Immunity, Journal of Computational Science, Volume 37, October 2019, 101027. DOI: 10.1016/j.jocs.2019.101027.
52. J.R. Yusupov, K.K. Sabirov, M. Ehrhardt and D.U. Matrasulov, Transparent nonlinear networks, Physical Review E, Vol. 100, No. 3 (September 2019), 032204. DOI: 10.1103/PhysRevE.100.032204.
53. S. Treibert, H. Brunner and M. Ehrhardt, Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis, Mathematical Biosciences and Engineering, 2019, 16(6), 7250-7298. DOI: 10.3934/mbe.2019364.
54. J.R. Yusupov, K.K. Sabirov, M. Ehrhardt and D.U. Matrasulov, Transparent Quantum Graphs, Physics Letters A, Volume 383, Issue 20 (July 2019), 2382-2388. DOI: 10.1016/j.physleta.2019.04.059
55. M.C. Calvo-Garrido, M. Ehrhardt and C. Vázquez, Jump-diffusion models with two stochastic factors for pricing swing options in electricity markets with partial-integro differential equations, Appl. Numer. Math. Vol. 139 (May 2019), 77-92. DOI: 10.1016/j.apnum.2019.01.001
56. I. Kossaczký, M. Ehrhardt and M. Günther, The Two-dimensional Tree-Grid Method, J. Comput. Finance Volume 23, Number 2 (September 2019), 29-57. DOI: 10.21314/JCF.2019.373
57. L. Teng, M. Ehrhardt and M. Günther, Quanto Pricing in Stochastic Correlation Models, Intl. J. of Theoret. & Appl. Finance Vol. 21, No. 05, 1850038 (2018).
58. G. Tauzin, L. Biferale, M. Sbragaglia, A. Gupta, F. Toschi, A. Bartel and M. Ehrhardt, A numerical tool for the study of the hydrodynamic recovery of the Lattice Boltzmann Method, Computers & Fluids Vol. 172, 30 August 2018, 241-250. DOI: 10.1016/j.compfluid.2018.05.031
59. L. Teng, M. Ehrhardt and M. Günther, Numerical Simulation of the Heston model under Stochastic Correlation, Int. J. Financial Stud. 2018, 6, 3. DOI: 10.3390/ijfs6010003.
60. I. Kossaczký, M. Ehrhardt and M. Günther, A new convergent explicit Tree-Grid Method for HJB equations in one space dimension, Numer. Math. Theor. Meth. Appl. Vol. 11, No. 1, Feb. 2018. DOI: 10.4208/nmtma.OA-2017-0066.
61. C. Hendricks, M. Ehrhardt and M. Günther, Hybrid finite difference / pseudospectral methods for the Heston and Heston-Hull-White PDE, J. Comput. Finance Vol. 21, No. 5 (April 2018), 1-33. DOI: 10.21314/JCF.2018.342.
62. D. Shcherbakov, M. Ehrhardt, J. Finkenrath, M. Günther, F. Knechtli and M. Peardon, Adapted Nested Force-Gradient Integrators: The Schwinger Model Case, Commun. Comput. Phys. Vol. 21, (2017), 1141-1153. DOI: 10.4208/cicp.OA-2016-0048.
63. C. Hendricks, C. Heuer, M. Ehrhardt and M. Günther, High-order ADI schemes for parabolic equations in the combination technique with application in finance, J. Comput. Appl. Math. 316 (2017), 175-194.
64. M.C. Calvo-Garrido, M. Ehrhardt and C. Vázquez, Pricing swing options in electricity markets with two stochastic factors using a partial differential equation approach, J. Comput. Finance 20(3) (2017), 81-107. DOI: 10.21314/JCF.2016.317
65. P. Petrov, D.V. Makarov and M. Ehrhardt, Wide-angle parabolic approximations for the nonlinear Helmholtz equation in the Kerr media, EPL, 116 (2016) 24004. DOI: 10.1209/0295-5075/116/24004
66. C. Besse, M. Ehrhardt and I. Lacroix-Violet, Discrete Artificial Boundary Conditions for the Korteweg de Vries equation, Numer. Meth. Part. Diff. Eqs. 32, Issue 5 (2016), 1455-1484. DOI: 10.1002/num.22058
67. C. Hendricks, M. Ehrhardt and M. Günther, Error splitting preservation for high order finite difference schemes in the combination technique, Numer. Math. Theor. Meth. Appl. Vol. 10, No. 3 (August 2017), 689-710. DOI: 10.4208/nmtma.2017.m1511
68. P. Petrov and M. Ehrhardt, Transparent boundary conditions for iterative high-order parabolic equations, J. Comput. Phys. Vol. 313 (May 2016), 144-158.
69. C. Hendricks, M. Ehrhardt and M. Günther, High-Order ADI schemes for diffusion equations with mixed derivatives in the combination technique, Appl. Numer. Math. Vol. 101, March 2016, 36-52.
70. L. Teng, M. Ehrhardt and M. Günther, On the Heston model with Stochastic Correlation, Int. J. Theoret. Appl. Fin. vol. 19(06), (2016) pages 1650033-01
71. I. Kossaczký, M. Ehrhardt and M. Günther, On the Non-Existence of Higher Order Monotone Approximation Schemes for HJB Equations, Appl. Math. Lett. Vol. 52, February 2016, 53-57.
72. L. Teng, M. Ehrhardt and M. Günther, Modelling Stochastic Correlation, Journal of Mathematics in Industry (SpringerOpen), 6:2, 2016.
73. D. Heubes, A. Bartel and M. Ehrhardt, Concept for a one-dimensional discrete artificial boundary condition for the lattice Boltzmann method, Comput. Math. Appl., Vol.70, Issue 10, November 2015, 2316-2330.
74. Z. Bučková, M. Ehrhardt and M. Günther, Alternating Direction Explicit Methods for Convection Diffusion Equations, Acta Math. Univ. Comenianae, 84(2) September 2015, 309-325.
75. C. Hendricks, M. Ehrhardt and M. Günther, High Order Combination Technique for the efficient Pricing of Basket Options, Acta Math. Univ. Comenianae, 84(2) September 2015, 243-253.
76. L. Teng, M. Ehrhardt and M. Günther, Option Pricing with dynamically correlated stochastic interest rate, Acta Math. Univ. Comenianae, 84(2) September 2015, 179-190.
77. L. Teng, C. van Emmerich, M. Ehrhardt and M. Günther, A Versatile Approach for Stochastic Correlation using Hyperbolic Functions, Int. J. Comput. Math., Vol. 93, Issue 3, 2016, 524-539.
78. P. Petrov and M. Ehrhardt, On Mayfield's stability proof for the discretized transparent boundary condition for the parabolic equation, Appl. Math. Lett. Vol. 44, June 2015, 45-49.
79. D. Shcherbakov, M. Ehrhardt, M. Günther and M. Peardon, Force-Gradient Nested Multirate Methods for Hamiltonian Systems, Comput. Phys. Commun. Vol. 187, February 2015, 91-97.
80. L. Teng, M. Ehrhardt and M. Günther, The pricing of Quanto options under dynamic correlation, J. Comput. Appl. Math. Vol. 275, February 2015, 304-310.
81. D. Heubes, A. Bartel and M. Ehrhardt, Exact Artificial Boundary Conditions for a Lattice Boltzmann Method, Comput. Math. Appl. Vol. 67 (2014), 2041-2054.
82. C. Hendricks and M. Ehrhardt, Evaluating the Effects of Changing Market Parameters and Policy Implications in the German Electricity Market, The Journal of Energy Markets Vol. 7, No. 2 (June 2014), 93-126. DOI: 10.21314/JEM.2014.115
83. I. Famelis, G. Galanis, M. Ehrhardt and D. Triantafyllou, Classical and Quasi-Newton methods for a Meteorological Parameters Prediction Boundary Value Problem, Appl. Math. Inf. Sci. Vol. 8, No. 6 (2014), 2683-2693. DOI: 10.12785/amis/080604
84. D. Heubes, A. Bartel and M. Ehrhardt, Characteristic Boundary Conditions in the Lattice Boltzmann Method for Fluid and Gas dynamics, J. Comput. Appl. Math. Vol. 262, (2014), 51-61.
85. J.-C. Cortés, M. Ehrhardt, A. Sánchez-Sánchez, F.-J. Santonja and R.-J. Villanueva, Modelling the dynamics of the students academic performance in the German region of North Rhine-Westphalia: an epidemiological approach with uncertainty, Int. J. Comput. Math. Vol. 91, Issue 2 (2014), 241-251.
86. L. Teng, M. Ehrhardt and M. Günther, Bilateral Counterparty Risk Valuation of CDS contracts with Simultaneous Defaults, Int. J. Theoret. Appl. Finance Vol. 16, Issue 07 (2013), 1350040.
87. M. Ehrhardt and R.E. Mickens, A Nonstandard Finite Difference Scheme for Convection-Diffusion Equations having Constant Coefficients, Appl. Math. Comput. Vol. 219, Issue 12 (2013), 6591-6604.
88. L. Teng, M. Ehrhardt and M. Günther, Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model, Int. J. Comput. Math. Vol. 90, Issue 5 (2013), 1083-1095.
89. G.I. Ramírez-Espinoza and M. Ehrhardt, Conservative and Finite Volume Methods for the convection-dominated Pricing Problem, Adv. Appl. Math. Mech. Vol. 5, Issue 6 (2013), 759-790.
90. Quang A Dang and M. Ehrhardt, On Dirac delta sequences and their generating functions, Appl. Math. Lett. Vol. 25, Issue 12 (2012), 2385-2390.
91. A. Arnold, M. Ehrhardt, M. Schulte and I. Sofronov, Discrete transparent boundary conditions for the Schrödinger equation on circular domains, Commun. Math. Sci. Vol. 10, Issue 3 (2012), 889-916.
92. Quang A Dang, M. Ehrhardt, Gia Lich Tran and Duc Le, Mathematical Modelling and Numerical Algorithms for Simulation of Oil Pollution, Environmental Modeling & Assessment Vol. 17, Issue 3 (2012), 275-288.
    (see also Erratum in Environmental Modeling & Assessment Vol. 17, Issue 4 (2012), Page 453)
93. M.H. Nguyen and M. Ehrhardt, Modelling and Numerical Valuation of Power Derivatives in Energy Markets, Adv. Appl. Math. Mech. Vol. 4, Number 3 (2012) 259-293.
94. P. Klein, X. Antoine, C. Besse and M. Ehrhardt, Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities, Commun. Comput. Phys. Vol. 10, Number 5, (2011), 1280-1304.
95. E. Dremkova and M. Ehrhardt, A high-order compact method for nonlinear Black-Scholes option pricing equations of American Options, Int. J. Comput. Math. Vol. 88, Issue 13, (2011), 2782-2797.
96. A. Mezentsev, A. Pomelnikov and M. Ehrhardt, Efficient Numerical Valuation of Continuous Installment Options, Adv. Appl. Math. Mech. Vol. 3, Number 2, (2011), 141-164.
97. M. Ehrhardt, Absorbing Boundary Conditions for Hyperbolic Systems, Numerical Mathematics: Theory, Methods and Applications Vol. 3, Number 3, (2010), 295-337. DOI: 10.4208/nmtma.2010.33.3.
98. L. Šumichrast and M. Ehrhardt, Comparison of the continuous, semi-discrete and fully-discrete transparent boundary conditions (TBC) for the parabolic wave equation 1. Theory, Journal of Electrical Engineering Vol. 60, Number 2, (2009), 301-312.
99. M. Ehrhardt, J. Sun and C. Zheng, Evaluation of scattering operators for semi-infinite periodic arrays, Commun. Math. Sci. Vol. 7, Issue 2 (2009), 347-364.
100. O. Gloger, M. Ehrhardt, Th. Dietrich, O. Hellwich, K. Graf and E. Nagel, A three stepped coordinated Level Set Segmentation Method for Identifying atherosclerotic plaques on MR-images, Commun. Numer. Meth. in Engng. Vol. 25, Issue 6, (2009), 615-638.
     • Coloured Images from the article can be seen here
101. M. Ehrhardt, H. Han and C. Zheng, Numerical simulation of waves in periodic structures, Commun. Comput. Phys. Vol. 5, Number 5, (2009), 849-870.
102. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt and A. Schädle, A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations, Commun. Comput. Phys. Vol. 4, Number 4, (2008), 729-796. (open-access article)
     supplementary material (Matlab codes):
     • MATLAB GUI
     • Talks from the ICIAM07 Minisymposium
103. M. Ehrhardt and C. Zheng, Exact artificial boundary conditions for problems with periodic structures, J. Comput. Phys. Vol. 227, Issue 14, (2008), 6877-6894.
104. M. Ehrhardt and R.E. Mickens, Discrete Models for the Cube-Root Differential Equation, Neural, Parallel, and Scientific Computations Vol. 16, Number 2, (2008), 179-188.
105. J. Ankudinova and M. Ehrhardt, On the numerical solution of nonlinear Black-Scholes equations, Comput. Math. Appl. Vol. 56, Number 3, (2008), 799-812.
106. A.G. Bratsos, M.  Ehrhardt and I.Th.  Famelis, A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations, Appl. Math. Comput. Vol. 197, Issue 1, (2008), 190-205.
     supplementary material (Mathematica codes):
     • ADM method for the continuous Schrödinger equation
     • ADM method for a semi-discrete Schrödinger equation (Example from paper)
107. A. Zisowsky and M. Ehrhardt, Discrete artificial boundary conditions for nonlinear Schrödinger equations, Math. Comput. Modell. Vol. 47, Issue 11-12, (2008), 1264-1283.
108. M. Ehrhardt, Discrete Transparent Boundary Conditions for Schrödinger-type equations for non-compactly supported initial data, Appl. Numer. Math. Vol. 58, Issue 5, (2008), 660-673.
109. M. Ehrhardt and R.E. Mickens, A fast, stable and accurate numerical method for the Black-Scholes equation of American options, Int. J. Theoret. Appl. Finance Vol. 11, Issue 5, (2008), 471-501.
     supplementary material:
     • Maple Code (Coefficients for sum-of-exponentials ansatz)
110. M. Ehrhardt and A. Zisowsky, Discrete non-local boundary conditions for Split-Step Padé Approximations of the One-Way Helmholtz Equation, J. Comput. Appl. Math., Vol. 200, Issue 2, (2007), 471-490.
111. Dang Quang A and M. Ehrhardt, Adequate Numerical Solution of Air Pollution problems by Positive Difference schemes on unbounded domains, Math. Comput. Modelling, Vol. 44, Issue 9-10, (2006), 834-856.
112. A. Zisowsky and M. Ehrhardt, Discrete Transparent Boundary Conditions for Parabolic Systems, Math. Comput. Modelling, Vol. 43, Issue 3-4, (2006), 294-309.
113. M. Ehrhardt and A. Zisowsky, Fast Calculation of Energy and Mass preserving solutions of Schrödinger-Poisson systems on unbounded domains, J. Comput. Appl. Math., Vol. 187, Issue 1, (2006), 1-28.
114. A. Zisowsky, A. Arnold, M. Ehrhardt and Th. Koprucki, Discrete Transparent Boundary Conditions for transient kp-Schrödinger Equations with Application to Quantum-Heterostructures, Journal of Applied Mathematics and Mechanics (ZAMM), Vol. 85, No. 11, (2005), 793-805.
115. M. Ehrhardt and R.E. Mickens, Solutions to the Discrete Airy Equation: Application to Parabolic Equation Calculations, J. Comput. Appl. Math., Vol. 172, Issue 1, (2004), 183-206.
116. A. Arnold, M. Ehrhardt and I. Sofronov, Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability, Comm. Math. Sci., Vol. 1, No. 3, (2003), 501-556.
     DOI: http://dx.doi.org/10.4310/CMS.2003.v1.n3.a7
     supplementary material:
     • Java-Applet (Transformation rule)
     • Maple Code (Coefficients for sum-of-exponentials ansatz)
117. M. Ehrhardt, Efficient Numerical Implementation of Discrete Transparent Boundary Conditions for Parabolic Equations in Underwater Acoustics, Acta Acustica united with Acustica, Volume 88 (2002), 711-713.
118. M. Ehrhardt and A. Arnold, Discrete Transparent Boundary Conditions for the Schrödinger Equation, Rivista di Mathematica della Universita di Parma, Volume 6, Number 4 (2001), 57-108.
119. M. Ehrhardt, Discrete Transparent Boundary Conditions for General Schrödinger-Type Equations, VLSI Design, Volume 9, Number 4 (1999), 325-338.
120. A. Arnold and M. Ehrhardt, Discrete Transparent Boundary Conditions for Wide Angle Parabolic Equations in Underwater Acoustics, Journal of Computational Physics, Volume 145, Number 2 (1998), 611-638.
     (List of known errata)

1. J. Ackermann, M. Ehrhardt, T. Kruse and A. Tordeux, Modelling car-following dynamics with stochastic input-state-output port-Hamiltonian systems, Proceedings of Traffic & Granular Flows 2024.
2. A. Clevenhaus, C. Totzeck and M. Ehrhardt, A numerical study of the impact of variance boundary conditions for the Heston model, in K. Burnecki, J. Szwabiński, and M. Teuerle (eds.) Progress in Industrial Mathematics at ECMI 2023, The European Consortium for Mathematics in Industry, Springer, 2024, pp ???. DOI: ???
3. T. Kossaczká, M. Ehrhardt and M. Günther, A Deep Smoothness WENO Method with Applications in Option Pricing, in: M. Ehrhardt and M. Günther (eds.), Progress in Industrial Mathematics at ECMI 2021, The European Consortium for Mathematics in Industry, Springer, 2022, pp 417-423. DOI: 10.1007/978-3-031-11818-0_54.
4. M. Muniz, M. Ehrhardt and M. Günther, Correlation Matrices driven by Stochastic Isospectral Flows, in: M. Ehrhardt and M. Günther (eds.), Progress in Industrial Mathematics at ECMI 2021, The European Consortium for Mathematics in Industry, Springer, 2022, pp. 455-461. DOI: 10.1007/978-3-031-11818-0_59.
5. A. Clevenhaus, M. Ehrhardt and M. Günther, The Parareal Algorithm and the Sparse Grid Combination Technique in the Application of the Heston Model, in: M. Ehrhardt and M. Günther (eds.), Progress in Industrial Mathematics at ECMI 2021, The European Consortium for Mathematics in Industry, Springer, 2022, pp. 477-483. DOI: 10.1007/978-3-031-11818-0_62.
6. J. Jäschke, M. Ehrhardt, M. Günther and B. Jacob, Discrete port-Hamiltonian Coupled Heat Transfer, in: M. Ehrhardt and M. Günther (eds.), Progress in Industrial Mathematics at ECMI 2021, The European Consortium for Mathematics in Industry, Springer, 2022, pp. 439-445. DOI: 10.1007/978-3-031-11818-0_57.
7. L. Kapllani, L. Teng and M. Ehrhardt, A Multistep Scheme to solve Backward Stochastic Differential Equations for Option Pricing on GPUs, in: I. Dimov and S. Fidanova (eds.), Advances in High Performance Computing, Results of the International Conference on "High Performance Computing" Borovets, Bulgaria, 2019, Studies in Computational Intelligence 902, Springer, 2021, pp. 196-208. DOI: 10.1007/978-3-030-55347-0
8. A.G. Tyshchenko, P.S. Petrov and M. Ehrhardt, Wide-angle mode parabolic equation with transparent boundary conditions and its applications in shallow water acoustics, Proceedings of the International Conference DAYS on DIFFRACTION 2019, St.Petersburg, Russia, 2019.
9. P. Petrov, A.G. Tyshchenko and M. Ehrhardt, Numerical solution of iterative parabolic equations approximating the nonlinear Helmholtz equation, Proceedings of the International Conference DAYS on DIFFRACTION 2018, St.Petersburg, Russia, 2018.
10. I. Kossaczký, M. Ehrhardt and M. Günther, The Tree-Grid Method with Control-Independent Stencil, in: (K. Mikula, D. Sevcovic, and J. Urban, eds.) Proceedings of Equadiff 2017 Conference, Bratislava, July 24-28, 2017, pp. 79-88.
11. P. Petrov, M. Ehrhardt and D.V. Makarov, Multiscale Approach to Parabolic Equations Derivation: Beyond the Linear Theory, Proceedings of ICCS 2017 International Conference on Computational Science, Zurich, 12-14 June, 2017, Procedia Computer Science, Volume 108, 2017, Pages 1823-1831. http://dx.doi.org/10.1016/j.procs.2017.05.085
12. H. Espinoza, R. Paredes and M. Ehrhardt, A New Two-Way Artificial Boundary Condition for Wave Propagation: Formulation and Benchmarking, 23rd AIAA/CEAS Aeroacoustics Conference, 2017 AIAA Aviation and Aeronautics Forum and Exposition, Colorado, 5-9 June 2017.
13. J.P. Silva, E.J.W. ter Maten, M. Günther and M. Ehrhardt, Reduced Models in Option Pricing, in: P. Quintela, P. Barral, D. Gómez, F.J. Pena, J. Rodriguez, P. Salgado, M.E. Vázquez-Méndez (Eds.): Progress in Industrial Mathematics at ECMI 2016, Santiago de Compostela, Springer, Series Mathematics in Industry, Vol. 26, 2017. ISBN 978-3-319-63081-6. DOI: http://dx.doi.org/10.1007/978-3-319-63082-3_23, 2017, pp. 161-168.
14. I. Kossaczký, M. Ehrhardt and M. Günther, Modifications of the PCPT Method for HJB Equations, Proceedings of AMiTaNS'16 - Eighth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 22-27, 2016, AIP Conference proceedings Vol. 1773, 030002 (2016). http://dx.doi.org/10.1063/1.4964962
15. Z. Bučková, P. Pólvora, M. Ehrhardt and M. Günther, Implementation of alternating direction explicit methods for higher dimensional Black-Scholes equations, Proceedings of AMiTaNS'16 - Eighth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 22-27, 2016, AIP Conference proceedings Vol. 1773, 030001 (2016). http://dx.doi.org/10.1063/1.4964961
16. C. Hendricks, C. Heuer, M. Ehrhardt and M. Günther, High-Order-Compact ADI schemes for pricing basket options in the combination technique, SCF 2015 Lisbon, Proceedings, July 2015.
17. P. Petrov and M. Ehrhardt, Transparent boundary conditions for the high-order parabolic approximations, Proceedings of the International Conference DAYS on DIFFRACTION 2015, St.Petersburg, Russia, May 25-29, 2015, pp. 255-260.
18. A. Arnold and M. Ehrhardt, A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics, In: I. Dimov, I. Farago, L. Vulkov (eds.) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science, Vol. 9045. Springer, Cham, 2015, pages 15-24.
19. D. Heubes, A. Bartel and M. Ehrhardt, Discrete Artificial Boundary Conditions for the Lattice Boltzmann Method in 2D, ESAIM proceedings of DSFD-2014, Volume 52, December 2015, pp. 47-65.
20. L. Teng, M. Ehrhardt and M. Günther, The Pricing of Quanto Options under Dynamic Correlation, in: (J. Vigo-Aguiar, ed.) Proceedings of the 14th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2014, July 3-7, 2014, Cadiz, Spain, Volume 1, pp. 1228-1238.
21. J. Silva, E.J.W. ter Maten, M. Günther and M. Ehrhardt, Proper Orthogonal Decomposition in Option Pricing: Basket Options and Heston Model, Proceedings of the 18th European Conference on Mathematics for Industry, June 9-13, 2014, Taormina, Italy, Springer Verlag, Berlin, Heidelberg, 2015.
22. C. Hendricks, M. Ehrhardt and M. Günther, Integrated Forecasting of day-ahead Prices in the German Electricity Market, Proceedings of the 18th European Conference on Mathematics for Industry, June 9-13, 2014, Taormina, Italy, Springer Verlag, Berlin, Heidelberg, 2015.
23. Z. Bučková, M. Ehrhardt and M. Günther, Fichera Theory and its Application in Finance, Proceedings of the 18th European Conference on Mathematics for Industry, June 9-13, 2014, Taormina, Italy, Springer Verlag, Berlin, Heidelberg, 2015.
24. J.-C. Cortés, M. Ehrhardt, A. Sánchez-Sánchez, F.-J. Santonja and R.-J. Villanueva, Modelling the dynamics of the students academic performance in the German region of North Rhine-Westphalia, Proceedings of the CMMSE 2012 - 12th International Conference Computational and Mathematical Methods in Science and Engineering, July 2-5, La Manga-Murcia, Spain.
25. A. Belova, M. Ehrhardt and T. Shmidt, Meshfree Methods in Option Pricing, Proceedings of the Mediterranean Conference on Embedded Computing, June 19-21, 2012, Bar, Montenegro, Advances and Challenges in Embedded Computing Vol. 1 (2012), pp. 242-245.
26. D. Shcherbakov and M. Ehrhardt, Multistep Methods for Lattice QCD Simulations, Proceedings of LATTICE 2011 - XXIX International Symposium on Lattice Field Theory, July 10-16, 2011, Squaw Valley, Lake Tahoe, California, USA. Proceedings of Science PoS (Lattice 2011), 327-333.
27. P. Klein, X. Antoine, C. Besse and M. Ehrhardt, Absorbing boundary conditions for solving stationary Schrödinger equations, Proceedings of the 16th European Conference on Mathematics for Industry, July 26-30, 2010, Wuppertal, Germany, Springer Verlag, Berlin, Heidelberg, 2011.
28. M. Ehrhardt, J. Fuhrmann, E. Holzbecher and A. Linke, Mathematical Modeling of Channel - Porous Layer Interfaces in PEM Fuel Cells, Proceedings of FDFC2008 - Fundamentals and Developments of Fuel Cell Conference 2008, Nancy, France, December 10-12, 2008, ISBN 978-2-7466-0413-1.
29. L. Šumichrast and M. Ehrhardt, Continuous, semi-discrete and fully-discrete formulation of the transparent boundary conditions for the beam propagation method, Proceedings of Advanced Aspects of Theoretical Electrical Engineering, Sozopol, Bulgaria, September, 22-25, 2007, pp. 139-152.
30. I.Th. Famelis, M. Ehrhardt and A.G. Bratsos, A discrete Adomian decomposition method for the discrete nonlinear Schrödinger equation, Proceedings of HERCMA 2007 - The 8th Hellenic European Research on Computer Mathematics & its Applications Conference, Athens, Greece, September, 20-22, 2007. (Session: Nonlinear Physical Phenomena: Some recent studies).
    supplementary material (Mathematica codes):
    • ADM method for the continuous Schrödinger equation
    • ADM method for a semi-discrete Schrödinger equation (Example from paper)
31. L. Šumichrast and M. Ehrhardt, On the three formulations of transparent boundaries for the beam propagation method, Proceedings of AMTEE 2007 - Advanced Methods of the Theory of Electrical Engineering (Applied to Power Systems), Pilsen, Czech Republic, September, 10-12, 2007.
32. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt and A. Schädle, A Review of Artificial Boundary Conditions for the Schrödinger Equation, Proceedings in Applied Mathematics and Mechanics (PAMM), Volume 7, Issue 1 (2007), 1023201-1023202, (Special Issue: ICIAM07 Minisymposia - 02 Numerical Analysis).
33. M. Ehrhardt and A. Zisowsky, Nonlocal Boundary Conditions for Higher-Order Parabolic Equations, Proceedings in Applied Mathematics and Mechanics (PAMM), Volume 6, Issue 1 (2006), 733-734, (Special Issue: GAMM Annual Meeting 2006).
34. M. Ehrhardt and A. Arnold, Discrete Transparent Boundary Conditions for Wide Angle Parabolic Equations: Fast Calculation and Approximation, Proceedings of the Seventh European Conference on Underwater Acoustics, July 3-8, 2004, Delft, The Netherlands, pp. 9-14.
35. A. Arnold, M. Ehrhardt and I. Sofronov, Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation, Proceedings of the 15th International Conference on Domain Decomposition Methods, July 21-25, 2003, Berlin, Germany, Lecture Notes in Computational Science and Engineering (LNCSE). Editors: R. Kornhuber, R.H.W. Hoppe, D.E. Keyes, J. Priaux, O. Pironneau, J. Xu.
36. M. Ehrhardt, Efficient Numerical Implementation of Discrete Transparent Boundary Conditions for Parabolic Equations, Proceedings of the Sixth European Conference on Underwater Acoustics, June 24-27, 2002, Gdansk, Poland, pp. 381-386.
    (List of known errata)
37. A. Arnold, M. Ehrhardt and I. Sofronov, A fast method to implement non-local discrete transparent boundary conditions for the Schrödinger equation, Proceedings of the GAMM 2002 Conference, March 25-28, 2002, Augsburg, Germany.
38. A. Arnold and M. Ehrhardt, Discrete Transparent Boundary Conditions for Wide Angle Parabolic Equations in Underwater Acoustics, Proceedings of the Fourth European Conference on Underwater Acoustics, September 21-25, 1998, Rome, Italy, pp. 769-774.
39. A. Arnold and M. Ehrhardt, A New Discrete Transparent Boundary Condition for Standard and Wide Angle ``Parabolic'' Equations in Underwater Acoustics, Proceedings of the Third International Conference on Theoretical and Computational Acoustics, July 14-18, 1997, Newark, New Jersey, USA, pp. 623-635.
40. M. Ehrhardt, Discrete Transparent Boundary Conditions for Parabolic Equations, Proceedings of the GAMM 96 Conference, ZAMM Volume 77 (1997), Supplement 2, S543-S544.

• M. Ehrhardt, Discrete Artificial Boundary Conditons, Ph.D. Thesis, Technische Universität Berlin, 2001.
  (Abstract) (Zusammenfassung) (List of known errata)

• M. Ehrhardt, Finite Differenzenverfahren für hyperbolische Systeme mit absorbierenden Randbedingungen, Diplomarbeit, Technische Universität Berlin, 1995. (Abstract) (PDF-Format)

• A. Arnold, M. Ehrhardt and S. Rjasanow, Numerik partieller Differentialgleichungen, Vorlesungsskript, Universität Saarbrücken, WS2001/02.

• S. Barbeiro, P. Csomós, M. Ehrhardt, J. Giesselmann, et al., Dynamics of and on networks: Numerics, control, applications, WG5 white paper, COST Action CA18232 - Mathematical models for interacting dynamics on networks, March 2024.
• M. Ehrhardt, M. Günther and W. Schilders, Erfolgsformeln (Success Formulas), November 2021.
  • L. Hartmer,  H. Krawczyk, Matthias Ehrhardt, Michael Günther, Wil Schilders: Erfolgsformeln - Anwendungen der Mathematik, Mathematische Semesterberichte 70 (2023), 63-68. DOI: 10.1007/s00591-022-00325-y.
• M. Ehrhardt, Die Formel des Glücks (The Formula of Happiness), Westdeutsche Zeitung, Wuppertal, 21. December 2017, p. 17.
• M. Ehrhardt, M. Günther and E. Jan W. ter Maten, ECMI SIG on Computational Finance, ECMI Newsletter 56, October 2014, pp. 20-22.
• Z. Bučková and M. Ehrhardt, Splitting Methods on Special Meshes, ECMI Newsletter 56, October 2014, pp. 71-72.
• Z. Bučková, J. Pedro Campos Moreira da Silva, M. Ehrhardt, M. Günther and E. Jan W. ter Maten, STRIKE : Novel Methods in Computational Finance - A European mathematical research training network, ECMI Newsletter 55, March 2014, pp. 9-11.
• M. Ehrhardt, A European Mathematics Network Against the Financial Crisis, BUW Output - Forschungsmagazin Research bulletin Nr. 9 der Bergischen Universität Wuppertal - Sommersemester, pp. 18-23, (31) May 2013.
• M. Ehrhardt, Beharrlichkeit 'zahlt' sich aus, Zum 25 jährigen Jubiläum, Bergische Blätter, 2011.
• M. Ehrhardt, Die Asymptotik der Schokoladen-Diät (The asymptotics of the chocolate diet), Chapter 7.2 in Besser als Mathe - Moderne angewandte Mathematik aus dem Matheon zum Mitmachen, Vieweg-Verlag, 2010, pages 238-248.