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...

ver descrição completa

Detalhes bibliográficos
Autores: Cano, Begoña, Moreta Santos, María Jesús
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
Descrição
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.