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Initial-Value Technique for Singularly Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations Arising in Chemical Reactor Theory

Author

Listed:
  • S. Natesan

    (Bharathidasan University)

  • N. Ramanujam

    (Bharathidasan University)

Abstract

An initial-value technique is presented for solving singularly perturbed two-point boundary-value problems for linear and semilinear second-order ordinary differential equations arising in chemical reactor theory. In this technique, the required approximate solution is obtained by combining solutions of two terminal-value problems and one initial-value problem which are obtained from the original boundary-value problem through asymptotic expansion procedures. Error estimates for approximate solutions are obtained. Numerical examples are presented to illustrate the present technique.

Suggested Citation

  • S. Natesan & N. Ramanujam, 1998. "Initial-Value Technique for Singularly Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations Arising in Chemical Reactor Theory," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 455-470, May.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:2:d:10.1023_a:1022639003366
    DOI: 10.1023/A:1022639003366
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Sahlan, M. Nosrati, 2019. "Four computational approaches for solving a class of boundary value problems arising in chemical reactor industry," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 253-268.
    4. S. Natesan & N. Ramanujam, 1998. "Booster Method for Singularly-Perturbed One-Dimensional Convection-Diffusion Neumann Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 53-72, October.
    5. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 0203, Economics Division, School of Social Sciences, University of Southampton.

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