Publication: A linearly implicit splitting method for solving time dependent semilinear reaction-diffusion systems
Date
Authors
Director
Publisher
Project identifier
Métricas Alternativas
Abstract
In this paper we deal with the efficient resolution of a coupled system of two one dimensional, time dependent, semilinear parabolic singularly perturbed partial differential equations of reaction-diffusion type, with distinct diffusion parameters which may have different orders of magnitude. The numerical method is based on a linearized version of the fractional implicit Euler method, which avoids the use of iterative methods, and a splitting by components to discretize in time; so, only tridiagonal linear systems are involved in the time integration process. Consequently, the computational cost of the proposed method is lower than classical schemes used for the same type of problems. The solution of this singularly perturbed problem features layers, what are resolved on an appropriate piecewise uniform mesh of Shishkin type. We show that the method is uniformly convergent of first order in time and of almost second order in space. Numerical results are presented to corroborate the theoretical results.
Description
Keywords
Department
Faculty/School
Degree
Doctorate program
item.page.cita
item.page.rights
© Springer Nature Switzerland AG 2020
Los documentos de Academica-e están protegidos por derechos de autor con todos los derechos reservados, a no ser que se indique lo contrario.