Solving reaction-diffusion problems with explicit Runge–Kutta exponential methods without order reduction
In this paper a technique is given to recover the classical order of the method when explicit exponential Runge–Kutta methods integrate reaction-diffusion problems. In the literature, methods of high enough stiff order for problems with vanishing boundary conditions have been constructed, but that i...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/112200 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/112200 |
| Access Level: | acceso abierto |
| Palavra-chave: | 519.6 Exponential Runge–Kutta methods Nonlinear reaction-diffusion problems Avoiding order reduction in time Matemáticas (Matemáticas) Análisis numérico 1206.13 Ecuaciones Diferenciales en Derivadas Parciales 1206 Análisis Numérico |
| Resumo: | In this paper a technique is given to recover the classical order of the method when explicit exponential Runge–Kutta methods integrate reaction-diffusion problems. In the literature, methods of high enough stiff order for problems with vanishing boundary conditions have been constructed, but that implies restricting the coefficients and thus, the number of stages and the computational cost may significantly increase with respect to other methods without those restrictions. In contrast, the technique which is suggested here is cheaper because it just needs, for any method, to add some terms with information only on the boundaries. Moreover, time-dependent boundary conditions are directly tackled here. |
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