, Volume 40, Issue 3, pp 305-322

Grid equidistribution for reaction–diffusion problems in one dimension

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Abstract

The numerical solution of a linear singularly-perturbed reaction–diffusion two-point boundary value problem is considered. The method used is adaptive movement of a fixed number of mesh points by monitor-function equidistribution. A partly heuristic argument based on truncation error analysis leads to several suitable monitor functions, but also shows that the standard arc-length monitor function is unsuitable for this problem. Numerical results are provided to demonstrate the effectiveness of our preferred monitor function.

Communicated by M. Gasca

AMS subject classification

Primary: 65L50; secondary: 65L10, 65L12, 65L70
Research supported by the Boole Centre for Research in Informatics, National University of Ireland, Cork, Ireland.
Natalia Kopteva: This paper was written while the first author was visiting the Department of Mathematics, National University of Ireland, Cork, Ireland.