Numerical Algorithms

, Volume 40, Issue 3, pp 305–322

Grid equidistribution for reaction–diffusion problems in one dimension

Article

DOI: 10.1007/s11075-005-7079-6

Cite this article as:
Kopteva, N., Madden, N. & Stynes, M. Numer Algor (2005) 40: 305. doi:10.1007/s11075-005-7079-6

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 problemsingular perturbationadaptive meshmonitor functionequidistribution

Copyright information

© 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