Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem


Cakir M.

ADVANCES IN DIFFERENCE EQUATIONS, 2010 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2010
  • Doi Number: 10.1155/2010/102484
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus

Abstract

We consider a singularly perturbed one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. The monotone operator is combined with the piecewise uniform Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. Numerical examples support the theoretical results.