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Initial-Value Technique for Singularly-Perturbed Turning-Point Problems Exhibiting Twin Boundary Layers

Author

Listed:
  • S. Natesan

    (Bharathidasan University)

  • M. Ramanujam

    (Bharathidasan University)

Abstract

The initial-value technique that was originally developed for solving singularly-perturbed nonturning-point problems (Ref. 1) is used here to solve singularly-perturbed turning-point problems exhibiting twin boundary layers. In this method, the required approximate solution is obtained by combining solutions of the reduced problem, an initial-value problem, and a terminal-value problem. Error estimates for approximate solutions are obtained. The implementation of the method on parallel architectures is discussed. Numerical examples are presented to illustrate the present technique.

Suggested Citation

  • S. Natesan & M. Ramanujam, 1998. "Initial-Value Technique for Singularly-Perturbed Turning-Point Problems Exhibiting Twin Boundary Layers," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 37-52, October.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:1:d:10.1023_a:1021744025980
    DOI: 10.1023/A:1021744025980
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    Cited by:

    1. Majumdar, Anirban & Natesan, Srinivasan, 2017. "Alternating direction numerical scheme for singularly perturbed 2D degenerate parabolic convection-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 453-473.
    2. T. Valanarasu & N. Ramanujam, 2007. "Asymptotic Initial-Value Method for Second-Order Singular Perturbation Problems of Reaction-Diffusion Type with Discontinuous Source Term," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 371-383, June.
    3. Singh, Satpal & Kumar, Devendra & Ramos, Higinio, 2022. "A uniformly convergent quadratic B-spline based scheme for singularly perturbed degenerate parabolic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 88-106.
    4. T. Valanarasu & N. Ramanujan, 2003. "Asymptotic Initial-Value Method for Singularly-Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 167-182, January.

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