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A Numerical Study on the Difference Solution of Singularly Perturbed Semilinear Problem with Integral Boundary Condition

    Musa Cakir Affiliation

Abstract

The present study is concerned with the numerical solution, using finite difference method on a piecewise uniform mesh (Shishkin type mesh) for a singularly perturbed semilinear boundary value problem with integral boundary condition. First we discuss the nature of the continuous solution of singularly perturbed differential problem before presenting method for its numerical solution. The numerical method is constructed on piecewise uniform Shishkin type mesh. We show that the method is first-order convergent in the discrete maximum norm, independently of singular perturbation parameter except for a logarithmic factor. We give effective iterative algorithm for solving the nonlinear difference problem. Numerical results which support the given estimates are presented.

Keyword : singular perturbation, exponentially fitted difference scheme, Shishkin mesh, uniformly convergence, integral boundary condition

How to Cite
Cakir, M. (2016). A Numerical Study on the Difference Solution of Singularly Perturbed Semilinear Problem with Integral Boundary Condition. Mathematical Modelling and Analysis, 21(5), 644-658. https://doi.org/10.3846/13926292.2016.1201702
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Sep 20, 2016
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This work is licensed under a Creative Commons Attribution 4.0 International License.