Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems

Autor:	Eugene O'Riordan, Grigorii I. Shishkin, M. L. Pickett
Rok vydání:	2006
Předmět:	Computational Mathematics Singular perturbation Algebra and Number Theory Partial differential equation Applied Mathematics Numerical analysis Uniform convergence Mathematical analysis Finite difference Finite difference method Convection–diffusion equation Numerical stability Mathematics
Zdroj:	Mathematics of Computation. 75:1135-1155
ISSN:	0025-5718
DOI:	10.1090/s0025-5718-06-01846-1
Popis:	In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0ee13fcfb668c39aacc62a7bd6c2c1c2 https://doi.org/10.1090/s0025-5718-06-01846-1 Zobrazit plný text záznamu