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An ε-Uniform Hybrid Scheme for Singularly Perturbed 1-D Reaction-Diffusion Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • S. Natesan

    (Indian Institute of Technology, Department of Mathematics)

  • R.K. Bawa

    (Punjabi University, Department of Computer Science and Engineering)

  • C. Clavero

    (Universidad de Zaragoza, Departamento de Matemática Aplicada)

Abstract

An ε-uniform second-order numerical method for singularly perturbed reaction-diffusion problems is proposed in this article. The difference scheme is based on cubic spline and classical finite difference scheme, which is applied on layer resolving Shishkin meshes. Uniform stability and uniform convergence of the scheme in the maximum norm are studied. A numerical example is presented to support the theoretical results.

Suggested Citation

  • S. Natesan & R.K. Bawa & C. Clavero, 2006. "An ε-Uniform Hybrid Scheme for Singularly Perturbed 1-D Reaction-Diffusion Problems," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 1079-1087, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_108
    DOI: 10.1007/978-3-540-34288-5_108
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