A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

Autor:	Anuradha Jha, Mohan K. Kadalbajoo
Rok vydání:	2014
Předmět:	Two parameter Discretization Logarithm Applied Mathematics Uniform convergence Mathematical analysis Finite difference method Perturbation (astronomy) Upwind scheme Backward Euler method Mathematics::Numerical Analysis Computer Science Applications Computational Theory and Mathematics Mathematics
Zdroj:	International Journal of Computer Mathematics. 92:1204-1221
ISSN:	1029-0265 0020-7160
Popis:	A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fee132ecb9299b43b5274c484bdad1de https://doi.org/10.1080/00207160.2014.928701 Zobrazit plný text záznamu