Paper Info
Title
Robust convergence of a compact fourth-order finite difference scheme for reaction–diffusion problems
Abstract
We consider a singularly perturbed one-dimensional reaction–diffusion problem with strong layers. The problem is discretized using a compact fourth order finite difference scheme. Altough the discretization is not inverse monotone we are able to establish its maximum-norm stability and to prove its pointwise convergence on a Shishkin mesh. The convergence is uniform with respect to the perturbation parameter. Numerical experiments complement our theoretical results.
Year
DOI
Venue
2008
10.1007/s00211-008-0184-4
Numerische Mathematik
Keywords
Field
DocType
diffusion problem,numerical experiment,compact fourth-order finite difference,inverse monotone,strong layer,order finite difference scheme,robust convergence,maximum-norm stability,perturbation parameter,pointwise convergence,one-dimensional reaction,shishkin mesh,65L10,65L12
Convergence (routing),Inverse,Discretization,Mathematical optimization,Mathematical analysis,Compact convergence,Pointwise convergence,Reaction–diffusion system,Mathematics,Monotone polygon,Perturbation (astronomy)
Journal
Volume
Issue
ISSN
111
2
0029-599X
Citations 
PageRank 
References 
5
0.64
1
Authors
1
Name
Order
Citations
PageRank
Torsten Linß16814.77