Uniformly convergent additive schemes for 2d singularly perturbed parabolic systems of reaction-diffusion type

Clavero, C. (Universidad de Zaragoza) ; Gracia, J.L. (Universidad de Zaragoza)

Resumen: In this work, we consider parabolic 2D singularly perturbed systems of reaction-diffusion type on a rectangle, in the simplest case that the diffusion parameter is the same for all equations of the system. The solution is approximated on a Shishkin mesh with two splitting or additive methods in time and standard central differences in space. It is proved that they are first-order in time and almost second-order in space uniformly convergent schemes. The additive schemes decouple the components of the vector solution at each time level of the discretization which makes the computation more efficient. Moreover, a multigrid algorithm is used to solve the resulting linear systems. Numerical results for some test problems are showed, which illustrate the theoretical results and the efficiency of the splitting and multigrid techniques.

Idioma: Inglés

DOI: 10.1007/s11075-018-0518-y

Año: 2019

Publicado en: Numerical Algorithms 80, 4 (2019), 1097-1120
ISSN: 1017-1398

Factor impacto JCR: 2.064 (2019)

Categ. JCR: MATHEMATICS, APPLIED rank: 39 / 260 = 0.15 (2019) - Q1 - T1

Factor impacto SCIMAGO: 1.143 - Applied Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/IUMA/MTM2017-83490-P
Financiación: info:eu-repo/grantAgreement/ES/MCYT-FEDER/MTM2016-75139-R

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)