A linearly implicit splitting method for solving time dependent semilinear reaction-diffusion systems
Fecha
2020Versión
Acceso abierto / Sarbide irekia
Tipo
Contribución a congreso / Biltzarrerako ekarpena
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.1007/978-3-030-41800-7_8
Resumen
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 ...
[++]
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. [--]
Materias
Linearly implicit splitting method,
Time dependent semilinear reaction-diffusion systems
Editor
Springer
Publicado en
Barrenechea, G., Mackenzie, J. (eds). Boundary and interior layers, computational and asymptotic methods, BAIL 2018. Lecture Notes in Computational Science and Engineering, vol 135. Springer, 2020, p. 129-141 978-3-030-41799-4
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute of Smart Cities - ISC