Métodos numéricos eficientes para problemas evolutivos de difusión-reacción con términos de reacción no lineales
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B. Bujanda [1] ; J.C. Jorge [2]
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[1] Universidad de La Rioja
Universidad de La Rioja
Logroño, España
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[2] Universidad Pública de Navarra
Universidad Pública de Navarra
Pamplona, España
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- Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals, Anastasio Pedro Santos Yanguas, 2001, ISBN 8469961446, págs. 599-600
- Idioma: español
- Texto completo no disponible (Saber más ...)
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Resumen
In this paper some new linearly implicit methods are designed to solve evolutionary diffusion-reaction problems with non linear reaction terms. Such methods combine the advantages of Alternating Direction Implicit methods and of the Additive Runge-Kutta methods introduced by Cooper & Sayfy (see [5]) to solve non linear stiff problems with linearly implicit schemes. These new methods have optimal order of computational complexity per time step and besides, under suitable smoothness requirements on the reaction terms, are unconditionally convergent. Some numerical experiences are shown confirming the expected efficiency and robustness of our methods, even integrating some singularly perturbed problems if suitable special meshes are used to discretize the spatial variables.
