| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 3205 - 3225 | |
| DOI | https://doi.org/10.1051/m2an/2025068 | |
| Published online | 01 December 2025 | |
Exponential Rosenbrock methods without order reduction when integrating nonlinear initial boundary value problems
1
Departamento de Matemática Aplicada, IMUVA, Universidad de Valladolid, Valladolid, Spain
2
Departamento de Análisis Económico y Economía Cuantitativa, IMUVA, Universidad Complutense de Madrid, Madrid, Spain
* Corresponding author: bcano@uva.es
Received:
18
March
2025
Accepted:
30
July
2025
A technique is described in this paper to avoid order reduction when integrating reaction-diffusion initial boundary value problems with explicit exponential Rosenbrock methods. The technique is valid for any Rosenbrock method, without having to impose any stiff order conditions, and for general time-dependent boundary values. An analysis on the global error is thoroughly performed and some numerical experiments are shown which corroborate the theoretical results, and in which a big gain in efficiency with respect to applying the standard method of lines can be observed.
Mathematics Subject Classification: 65M12 / 65M20
Key words: Exponential Rosenbrock methods / nonlinear reaction-diffusion problems / avoiding order reduction in time
© The authors. Published by EDP Sciences, SMAI 2025
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