Journal of Applied Mathematics (Jan 2010)

A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

  • Musa Çakır,
  • Gabil M. Amiraliyev

DOI
https://doi.org/10.1155/2010/495184
Journal volume & issue
Vol. 2010

Abstract

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The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter ε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.