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Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids

Author

Listed:
  • M.K. Kadalbajoo

    (Indian Institute of Technology)

  • K.C. Patidar

    (Indian Institute of Technology)

Abstract

A numerical method based on cubic splines with nonuniform grid is given for singularly-perturbed nonlinear two-point boundary-value problems. The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for the linear case using a variable-mesh cubic spline and are used to solve each linear equation obtained via quasilinearization. Second-order uniform convergence is achieved. Numerical examples are given in support of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:3:d:10.1023_a:1016023012671
    DOI: 10.1023/A:1016023012671
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    Cited by:

    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. 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.
    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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