Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis (AMNA)

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Books (8)

  1. L. Teng, M. Ehrhardt and M. Günther, Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance, World Scientific, scheduled 2020.
  2. M. Ehrhardt and M. Günther, Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Techno- und Wirtschaftsmathematik, Springer, scheduled 2019.
  3. T. Jax, A. Bartel, M. Ehrhardt, M. Günther and G. Steinebach, (eds.), Rosenbrock-Wanner-Type Methods: Theory and Applications, Springer, 2018.
  4. 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.
  5. M. Ehrhardt (ed.), Mathematical Modelling and Numerical Simulation of Oil Pollution Problems, Vol. 2 of the Springer series The Reacting Atmosphere, March 2015.
  6. M. Ehrhardt and Th. Koprucki (eds.), Advanced Mathematical Models and Numerical Techniques for Multiband Effective Mass Approximations, LNCSE, Vol. 94, Springer Verlag, Heidelberg, 2014.
  7. 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.
  8. M. Ehrhardt (ed.), Coupled Fluid Flow in Energy, Biology and Environmental Research, Progress in Computational Physics, Vol. 2, Bentham Science Publishers Ltd., 2012.
  9. 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.
  10. 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
  11. M. Ehrhardt, Discrete Artificial Boundary Conditions, Verlag dissertation.de, Berlin, 2001.

Special Issues (7)

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.

Chapter in Books (22)

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.), Advanced Mathematical Models and Numerical Techniques for Multiband Effective Mass Approximations, Springer Verlag, Heidelberg, 2014.
  11. 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.), Advanced Mathematical Models and Numerical Techniques for Multiband Effective Mass Approximations, Springer Verlag, Heidelberg, 2014.
  12. 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
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.

Articles in Journals (71)

  1. L. Teng, X. Wu, M. Günther and M. Ehrhardt, A new methodology to create valid time-dependent correlation matrices via isospectral flows, accepted: ESAIM: Mathematical Modelling and Numerical Analysis. 2019. DOI:10.1051/m2an/2019064
  2. M. Ehrhardt, J. Gašper and S. Kilianová, SIR-based Mathematical Modeling of Infectious Diseases with Vaccination and Waning Immunity, Journal of Computational Science, 2019. DOI:10.1016/j.jocs.2019.101027
  3. 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
  4. 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 (open access)
  5. 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
  6. 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
  7. I. Kossaczký, M. Ehrhardt and M. Günther, The Two-dimensional Tree-Grid Method, J. Comput. Finance, August 2019. DOI:10.21314/JCF.2019.373
  8. 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).
  9. 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
  10. 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 (open access)
  11. 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
  12. 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
  13. 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
  14. 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.
  15. 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
  16. 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
  17. 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
  18. 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.
  19. DOI: 10.4208/nmtma.2017.m1511
  20. P. Petrov and M. Ehrhardt, Transparent boundary conditions for iterative high-order parabolic equations, J. Comput. Phys. Vol. 313 (May 2016), 144-158.
  21. 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.
  22. 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
  23. 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.
  24. L. Teng, M. Ehrhardt and M. Günther, Modelling Stochastic Correlation, Journal of Mathematics in Industry (SpringerOpen), 6:2, 2016.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. D. Heubes, A. Bartel and M. Ehrhardt, Exact Artificial Boundary Conditions for a Lattice Boltzmann Method, Comput. Math. Appl. Vol. 67 (2014), 2041-2054.
  34. 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, June 2014.
  35. 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), 1-11.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42. Quang A Dang and M. Ehrhardt, On Dirac delta sequences and their generating functions, Appl. Math. Lett. Vol. 25, Issue 12 (2012), 2385-2390.
  43. 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.
  44. 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)
  45. 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.
  46. 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.
  47. 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.
  48. 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.
  49. M. Ehrhardt, Absorbing Boundary Conditions for Hyperbolic Systems, Numerical Mathematics: Theory, Methods and Applications Vol. 3, Number 3, (2010), 295-337.
  50. 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.
  51. 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.
  52. 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
  53. M. Ehrhardt, H. Han and C. Zheng, Numerical simulation of waves in periodic structures, Commun. Comput. Phys. Vol. 5, Number 5, (2009), 849-870.
  54. 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):
  55. M. Ehrhardt and C. Zheng, Exact artificial boundary conditions for problems with periodic structures, J. Comput. Phys. Vol. 227, Issue 14, (2008), 6877-6894.
  56. 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.
  57. J. Ankudinova and M. Ehrhardt, On the numerical solution of nonlinear Black-Scholes equations, Comput. Math. Appl. Vol. 56, Number 3, (2008), 799-812.
  58. 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):
  59. A. Zisowsky and M. Ehrhardt, Discrete artificial boundary conditions for nonlinear Schrödinger equations, Math. Comput. Modell. Vol. 47, Issue 11-12, (2008), 1264-1283.
  60. 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.
  61. 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)
  62. 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.
  63. 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.
  64. A. Zisowsky and M. Ehrhardt, Discrete Transparent Boundary Conditions for Parabolic Systems, Math. Comput. Modelling, Vol. 43, Issue 3-4, (2006), 294-309.
  65. 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.
  66. 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.
  67. 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.
  68. 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:
  69. 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.
  70. 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.
  71. M. Ehrhardt, Discrete Transparent Boundary Conditions for General Schrödinger-Type Equations, VLSI Design, Volume 9, Number 4 (1999), 325-338.
  72. 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)

Proceedings (33)

  1. 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.
  2. 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.
  3. 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.
  4. 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
  5. 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.
  6. 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.
  7. 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
  8. 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
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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):
  24. 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.
  25. 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).
  26. 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).
  27. 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.
  28. 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.
  29. 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)
  30. 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.
  31. 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.
  32. 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.
  33. M. Ehrhardt, Discrete Transparent Boundary Conditions for Parabolic Equations, Proceedings of the GAMM 96 Conference, ZAMM Volume 77 (1997), Supplement 2, S543-S544.

Ph.D. Thesis

Masters Thesis (in german)

Lecture Notes

Miscellaneous

  • 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.


University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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