Numerical Algorithms

, Volume 40, Issue 3, pp 305–322 | Cite as

Grid equidistribution for reaction–diffusion problems in one dimension

Article

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.

Keywords

reaction–diffusion problem singular perturbation adaptive mesh monitor function equidistribution 

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© Springer 2005

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland
  3. 3.Department of MathematicsNational University of IrelandCorkIreland

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