Uniformly convergent numerical method for singularly perturbed convection‐diffusion type problems with nonlocal boundary condition

Abstract

SummaryIn this article, we consider a class of singularly perturbed differential equations of convection‐diffusion type with nonlocal boundary conditions. A uniformly convergent numerical method is constructed via nonstandard finite difference and numerical integration methods to solve the problem. The nonlocal boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ϵ‐uniformly convergent.