Uniformly-Convergent Numerical Methods for a System of Coupled Singularly Perturbed Convection–Diffusion Equations with Mixed Type Boundary Conditions

Abstract

In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection - diffusion second order ordinary differential equations subject to the mixed type boundary conditions. We prove that the method has almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and also the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

Keywords:

• singular perturbation problems
• weakly coupled system
• piecewise uniform meshes
• scaled derivative
• finite difference scheme
• mid-point scheme
• cubic spline scheme

AMS Subject Classification:

• 65L10
• CR G1.7