Numerical solution of a singularly perturbed three-point boundary value problem


CAKIR M., Amiraliyev G.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.84, no.10, pp.1465-1481, 2007 (SCI-Expanded) identifier identifier

Abstract

We consider a uniform finite difference method on an S-mesh (Shishkin type mesh) for a singularly perturbed semilinear one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. We show that the method is first-order convergent in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. An effective iterative algorithm for solving the non-linear difference problem and some numerical results are presented.