Hoang, Manh Tuan; Ehrhardt, Matthias A general class of second-order \(L\)-stable explicit numerical methods for stiff problems. (English) Zbl 07782646 Appl. Math. Lett. 149, Article ID 108897, 7 p. (2024). MSC: 65L04 34A34 65L06 PDFBibTeX XMLCite \textit{M. T. Hoang} and \textit{M. Ehrhardt}, Appl. Math. Lett. 149, Article ID 108897, 7 p. (2024; Zbl 07782646) Full Text: DOI
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin PINN training using biobjective optimization: the trade-off between data loss and residual loss. (English) Zbl 07696976 J. Comput. Phys. 488, Article ID 112211, 21 p. (2023). MSC: 65Mxx 68Txx 90Cxx PDFBibTeX XMLCite \textit{F. Heldmann} et al., J. Comput. Phys. 488, Article ID 112211, 21 p. (2023; Zbl 07696976) Full Text: DOI arXiv
Berkhahn, Sarah; Ehrhardt, Matthias A physics-informed neural network to model COVID-19 infection and hospitalization scenarios. (English) Zbl 07636107 Adv. Contin. Discrete Models 2022, Paper No. 61, 27 p. (2022). MSC: 39-XX 34-XX PDFBibTeX XMLCite \textit{S. Berkhahn} and \textit{M. Ehrhardt}, Adv. Contin. Discrete Models 2022, Paper No. 61, 27 p. (2022; Zbl 07636107) Full Text: DOI
Arnold, Anton; Ehrhardt, Matthias A transparent boundary condition for an elastic bottom in underwater acoustics. (English) Zbl 1453.76198 Dimov, Ivan (ed.) et al., Finite difference methods, theory and applications. 6th international conference, FDM 2014, Lozenetz, Bulgaria, June 18–23, 2014. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 9045, 15-24 (2015). MSC: 76Q05 86A05 35J05 PDFBibTeX XMLCite \textit{A. Arnold} and \textit{M. Ehrhardt}, Lect. Notes Comput. Sci. 9045, 15--24 (2015; Zbl 1453.76198) Full Text: DOI
Klindworth, Dirk; Ehrhardt, Matthias; Koprucki, Thomas Discrete transparent boundary conditions for multi-band effective mass approximations. (English) Zbl 1309.82009 Ehrhardt, Matthias (ed.) et al., Multi-band effective mass approximations. Advanced mathematical models and numerical techniques. Cham: Springer (ISBN 978-3-319-01426-5/hbk; 978-3-319-01427-2/ebook). Lecture Notes in Computational Science and Engineering 94, 273-318 (2014). MSC: 82-08 82D80 82D37 65N06 PDFBibTeX XMLCite \textit{D. Klindworth} et al., Lect. Notes Comput. Sci. Eng. 94, 273--318 (2014; Zbl 1309.82009) Full Text: DOI
Dremkova, E.; Ehrhardt, M. A high-order compact method for nonlinear Black-Scholes option pricing equations of American options. (English) Zbl 1237.91228 Int. J. Comput. Math. 88, No. 13, 2782-2797 (2011). MSC: 91G60 91G20 65M06 65M12 65N06 PDFBibTeX XMLCite \textit{E. Dremkova} and \textit{M. Ehrhardt}, Int. J. Comput. Math. 88, No. 13, 2782--2797 (2011; Zbl 1237.91228) Full Text: DOI
Ankudinova, Julia; Ehrhardt, Matthias On the numerical solution of nonlinear Black-Scholes equations. (English) Zbl 1155.65367 Comput. Math. Appl. 56, No. 3, 799-812 (2008). MSC: 65M06 60H15 91G60 PDFBibTeX XMLCite \textit{J. Ankudinova} and \textit{M. Ehrhardt}, Comput. Math. Appl. 56, No. 3, 799--812 (2008; Zbl 1155.65367) Full Text: DOI
Ehrhardt, Matthias; Zisowsky, Andrea Discrete non-local boundary conditions for split-step Padé approximations of the one-way Helmholtz equation. (English) Zbl 1115.65120 J. Comput. Appl. Math. 200, No. 2, 471-490 (2007). MSC: 65N35 PDFBibTeX XMLCite \textit{M. Ehrhardt} and \textit{A. Zisowsky}, J. Comput. Appl. Math. 200, No. 2, 471--490 (2007; Zbl 1115.65120) Full Text: DOI
Ehrhardt, Matthias; Zisowsky, Andrea Fast calculation of energy and mass preserving solutions of Schrödinger-Poisson systems on unbounded domains. (English) Zbl 1082.65082 J. Comput. Appl. Math. 187, No. 1, 1-28 (2006). MSC: 65M06 35Q40 PDFBibTeX XMLCite \textit{M. Ehrhardt} and \textit{A. Zisowsky}, J. Comput. Appl. Math. 187, No. 1, 1--28 (2006; Zbl 1082.65082) Full Text: DOI
Ehrhardt, Matthias; Mickens, Ronald E. Solutions to the discrete Airy equation: application to parabolic equation calculations. (English) Zbl 1060.65092 J. Comput. Appl. Math. 172, No. 1, 183-206 (2004). Reviewer: Leonid B. Chubarov (Novosibirsk) MSC: 65M06 81Q05 35K55 35Q55 76Q05 76M20 65M12 PDFBibTeX XMLCite \textit{M. Ehrhardt} and \textit{R. E. Mickens}, J. Comput. Appl. Math. 172, No. 1, 183--206 (2004; Zbl 1060.65092) Full Text: DOI