Resumen de Métodos numéricos eficientes para problemas evolutivos de difusión-reacción con términos de reacción no lineales
Blanca Bujanda Cirauqui, Juan Carlos Jorge Ulecia
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.
