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Uniform Global Convergence of a Hybrid Scheme for Singularly Perturbed Reaction–Diffusion Systems

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  • S. C. S. Rao

    (Indian Institute of Technology Delhi)

  • S. Kumar

    (Indian Institute of Technology Delhi)

  • M. Kumar

    (Indian Institute of Technology Delhi)

Abstract

We consider a system of coupled singularly perturbed reaction–diffusion two-point boundary-value problems. A hybrid difference scheme on a piecewise-uniform Shishkin mesh is constructed for solving this system, which generates better approximations to the exact solution than the classical central difference scheme. Moreover, we prove that the method is third order uniformly convergent in the maximum norm when the singular perturbation parameter is small. Numerical experiments are conducted to validate the theoretical results.

Suggested Citation

  • S. C. S. Rao & S. Kumar & M. Kumar, 2011. "Uniform Global Convergence of a Hybrid Scheme for Singularly Perturbed Reaction–Diffusion Systems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 338-352, November.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9867-6
    DOI: 10.1007/s10957-011-9867-6
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    References listed on IDEAS

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    1. S. C. S. Rao & S. Kumar & M. Kumar, 2010. "A Parameter-Uniform B-Spline Collocation Method for Singularly Perturbed Semilinear Reaction-Diffusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 795-809, September.
    2. M.K. Kadalbajoo & K.C. Patidar, 2002. "Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 573-591, September.
    3. S. C. S. Rao & M. Kumar, 2007. "B-Spline Collocation Method for Nonlinear Singularly-Perturbed Two-Point Boundary-Value Problems," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 91-105, July.
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