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

• Published in: Mathematical modelling and analysis Vol. 21; no. 5; pp. 644 - 658
• Main Author: Cakir, Musa
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.09.2016; Vilnius Gediminas Technical University
• Subjects: Boundary conditions; Boundary value problems; exponentially fitted difference scheme; Finite difference method; Finite element method; integral boundary condition; Integrals; Linear equations; Mathematical analysis; Mathematical models; Mathematical research; Norms; Perturbation theory; Shishkin mesh; Singular perturbation; uniformly convergence; integral boundary condition; Shishkin mesh; singular perturbation; exponentially fitted difference scheme; uniformly convergence
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/13926292.2016.1201702

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.