Year: 2008
Author: Relja Vulanović
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 2 : pp. 235–244
Abstract
The paper is concerned with strongly nonlinear singularly perturbed boundary value problems in one dimension. The problems are solved numerically by finite-difference schemes on special meshes which are dense in the boundary layers. The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed. For the central scheme, error estimates are derived in a discrete $L^1$ norm. They are of second order and decrease together with the perturbation parameter ε. The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically. Numerical results show ε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-NMTMA-6050
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 2 : pp. 235–244
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Boundary-value problem singular perturbation finite differences Bakhvalov and piecewise equidistant meshes $L^1$ stability.