Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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HYBRID DIFFERENCE SCHEMES FOR SINGULARLY PERTURBED PROBLEM OF MIXED TYPE WITH DISCONTINUOUS SOURCE TERM

  • Priyadharshini, R. Mythili (Department of Mathematics, School of Mathematics and Computer Science, Bharathidasn University) ;
  • Ramanujam, N. (Department of Mathematics, School of Mathematics and Computer Science, Bharathidasn University) ;
  • Valanarasu, T. (Department of Mathematics, Bharathidasan University College)
  • Received : 2009.09.29
  • Accepted : 2009.11.13
  • Published : 2010.09.30
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Abstract

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.

Keywords

References

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