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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

    Natalia Kopteva

  2. Department of Mathematics, National University of Ireland, Galway, Ireland

    Niall Madden

  3. Department of Mathematics, National University of Ireland, Cork, Ireland

    Martin Stynes

Authors
  1. Natalia Kopteva
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  2. Niall Madden
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  3. Martin Stynes
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Corresponding author

Correspondence to Natalia Kopteva.

Additional information

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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Kopteva, N., Madden, N. & Stynes, M. Grid equidistribution for reaction–diffusion problems in one dimension. Numer Algor 40, 305–322 (2005). https://doi.org/10.1007/s11075-005-7079-6

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  • DOI: https://doi.org/10.1007/s11075-005-7079-6

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