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Grid equidistribution for reaction–diffusion problems in one dimension
 Natalia Kopteva,
 Niall Madden,
 Martin Stynes
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The numerical solution of a linear singularlyperturbed reaction–diffusion twopoint boundary value problem is considered. The method used is adaptive movement of a fixed number of mesh points by monitorfunction equidistribution. A partly heuristic argument based on truncation error analysis leads to several suitable monitor functions, but also shows that the standard arclength 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.
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 Title
 Grid equidistribution for reaction–diffusion problems in one dimension
 Journal

Numerical Algorithms
Volume 40, Issue 3 , pp 305322
 Cover Date
 20051101
 DOI
 10.1007/s1107500570796
 Print ISSN
 10171398
 Online ISSN
 15729265
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 reaction–diffusion problem
 singular perturbation
 adaptive mesh
 monitor function
 equidistribution
 Industry Sectors
 Authors

 Natalia Kopteva ^{(001)}
 Niall Madden ^{(002)}
 Martin Stynes ^{(003)}
 Author Affiliations

 001. Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
 002. Department of Mathematics, National University of Ireland, Galway, Ireland
 003. Department of Mathematics, National University of Ireland, Cork, Ireland