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Uniform Convergence of Finite-Difference Schemes for Reaction-Diffusion Interface Problems

  • Ivanka T. Angelova
  • Lubin G. Vulkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)

Abstract

We consider a singularly perturbed reaction-diffusion equation in two dimensions (x,y) with concentrated source on a segment parallel to axis Oy. By means of an appropriate (including corner layer functions) decomposition, we describe the asymptotic behavior of the solution. Finite difference schemes for this problem of second and fourth order of local approximation on Shishkin mesh are constructed. We prove that the first scheme is almost second order uniformly convergent in the maximal norm. Numerical experiments illustrate the theoretical order of convergence of the first scheme and almost fourth order of convergence of the second scheme.

Keywords

reaction-diffusion interface problems singular perturbation uniform convergence Shishkin mesh 

2000 Mathematics Subject Classification

65M06 65M12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ivanka T. Angelova
    • 1
  • Lubin G. Vulkov
    • 1
  1. 1.Department of MathematicsUniversity of RousseRousseBulgaria

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