A Numerical Study on the Difference Solution of Singularly Perturbed Semilinear Problem with Integral Boundary Condition. Issue 5 (2nd September 2016)

• Record Type: Journal Article
• Authors: Cakir, Musa
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 5(2016)
• Page Start: 644
• Page End: 658
• Publication Date: 2016-09-02
• Subjects: singular perturbation -- exponentially fitted difference scheme -- Shishkin mesh -- uniformly convergence -- integral boundary condition; 34D15 -- 65L05 -- 65L12 -- 65L20 -- 65L70; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1201702
• Languages: English
• ISSNs: 1392-6292

Abstract

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.