Open Access
Issue
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
Page(s) 495 - 515
DOI https://doi.org/10.1051/m2an/2026009
Published online 24 March 2026
  1. I. Alonso-Mallo, B. Cano and N. Reguera, Avoiding order reduction when integrating linear initial boundary value problems with exponential splitting methods. IMA J. Numer. Anal. 38 (2018) 1294–1323. [Google Scholar]
  2. I. Alonso-Mallo, B. Cano and N. Reguera, Avoiding order reduction when integrating reaction-diffusion boundary value problems with exponential splitting methods. J. Comput. Appl. Math. 357 (2019) 228–250. [CrossRef] [MathSciNet] [Google Scholar]
  3. I. Alonso-Mallo, B. Cano and N. Reguera, Comparison of efficiency among different techniques to avoid order reduction with Strang splitting. Numer. Methods Partial Differ. Eq. 37 (2021) 854–873. [Google Scholar]
  4. M. Caliari, F. Cassini, L. Einkemmer and A. Ostermann, On the convergence of split exponential integrators for semilinear parabolic problems. Preprint arXiv: 2503.16210 (2025). [Google Scholar]
  5. M. Crouzeix and V. Thomée, On the discretization in time of semilinear parabolic equations with nonsmooth initial data. Math. Comp. 49 (1987) 359–377. [Google Scholar]
  6. H. Dai, Q. Huang and C. Wang, Exponential time differencing-Padé finite element method for nonlinear convection-diffusion-reaction equations with time constant delay. J. Comput. Math. 41 (2023) 370–394. [Google Scholar]
  7. L. Einkemmer and A. Ostermann, Overcoming order reduction in diffusion-reaction splitting. Part 1: Dirichlet boundary conditions. SIAM J. Sci. Comput. 37 (2015) A1577–A1592. [CrossRef] [Google Scholar]
  8. L. Einkemmer and A. Ostermann, Overcoming order reduction in diffusion-reaction splitting. Part 2: oblique boundary conditions. SIAM J. Sci. Comput. 38 (2016) A3741–A3757. [CrossRef] [Google Scholar]
  9. C.M. Elliott and S. Larsson, Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation. Math. Comp. 58 (1992) 603–630. [CrossRef] [MathSciNet] [Google Scholar]
  10. K.-J. Engel, R. Nagel and S. Brendle, One-parameter Semigroups for Linear Evolution Equations. Vol. 194. Springer (2000). [Google Scholar]
  11. E. Faou, A. Ostermann and K. Schratz, Analysis of exponential splitting methods for inhomogeneous parabolic equations. IMA J. Numer. Anal. 35 (2015) 161–178. [CrossRef] [MathSciNet] [Google Scholar]
  12. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer (1977). [Google Scholar]
  13. D. Henry, Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics. Springer, Berlin, Heidelberg (1981). [Google Scholar]
  14. M. Hochbruck and A. Ostermann, Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43 (2005) 1069–1090. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Hochbruck and A. Ostermann, Exponential Runge-Kutta methods for parabolic problems. Appl. Numer. Math. 53 (2005) 323–339. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Hochbruck and A. Ostermann, Exponential integrators. Acta Numer. 19 (2010) 209–286. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Hochbruck and A. Ostermann, Exponential multistep methods of Adams-type. BIT Numer. Math. 51 (2011) 889–908. [Google Scholar]
  18. M. Hochbruck, A. Ostermann and J. Schweitzer, Exponential Rosenbrock-type methods. SIAM J. Numer. Anal. 47 (2009) 786–803. [CrossRef] [Google Scholar]
  19. Q. Huang, Z. Qiao and H. Yang, Maximum bound principle and non-negativity preserving ETD schemes for a phase field model of prostate cancer growth with treatment. Comput. Methods Appl. Mech. Eng. 426 (2024) 116981. [Google Scholar]
  20. S. Larsson, Nonsmooth data error estimates with applications to the study of the long-time behavior of finite element solutions of semilinear parabolic problems. Technical report, Dept. of Mathematics, Chalmers Univ. Göteborg (1992). [Google Scholar]
  21. B. Li and S. Ma, A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data. J. Sci. Comput. 87 (2021) 23. [Google Scholar]
  22. V.T. Luan and A. Ostermann, Exponential B-series: the stiff case. SIAM J. Numer. Anal. 51 (2013) 3431–3445. [Google Scholar]
  23. C. Lubich and A. Ostermann, Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: nonsmooth-data error estimates and applications to long-time behaviour. Appl. Numer. Math. 22 (1996) 279–292. [Google Scholar]
  24. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems. Birkhäuser, Berlin (1995). [Google Scholar]
  25. A. Ostermann, F. Saedpanah and N. Vaisi, Explicit exponential Runge-Kutta methods for semilinear integro-differential equations. SIAM J. Numer. Anal. 61 (2023) 1405–1425. [Google Scholar]
  26. A. Ostermann and M. Thalhammer, Non-smooth data error estimates for linearly implicit Runge-Kutta methods. IMA J. Numer. Anal. 20 (2000) 167–184. [Google Scholar]
  27. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (2012). [Google Scholar]
  28. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam (1978). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you