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The Error Analysis of Finite Difference Approximation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations with Discontinuous Source Term

  • S. Chandra Sekhara RaoEmail author
  • Sheetal Chawla
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

We consider a coupled system of two singularly perturbed semilinear reaction-diffusion equations with a discontinuous source term. The leading term in each equation is multiplied by a small positive parameter, but these parameters have different order of magnitude. The solution of these system of equations have overlapping and interacting boundary and interior layers. Based on the discrete Green’s function theory, the properties of the discretized operator are established. The error estimates are derived in the maximum norm for a central difference scheme on layer-adapted meshes, and the method is proved to be almost second order uniformly convergent independently of both the perturbation parameters. Numerical results validate the theoretical results.

Keywords

Singular perturbation Semilinear Coupled system Discontinuous source term Uniformly convergent Shishkin mesh Interior layers Discrete Green’s function 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia

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