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

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.

Keywords:

• Finite difference
• Singular perturbation
• Shishkin mesh
• Non-local boundary condition

Acknowledgements

The authors are grateful to the referees for their comments and suggestions which helped improve the quality of manuscript.