A New Second-Order Difference Approximation for Nonlocal Boundary Value Problem With Boundary Layers

Abstract

The aim of this paper is to present finite difference method for numerical solution of singularly perturbed linear differential equation with nonlocal boundary condition. Initially, the nature of the solution of the presented problem for the numerical solution is discussed. Subsequently, the difference scheme is established on Bakhvalov-Shishkin mesh. Uniform convergence in the second-order is proven with respect to the ε− perturbation parameter in the discrete maximum norm. Finally, an example is provided to demonstrate the success of the presented numerical method. Thus, it is shown that indicated numerical results support theoretical results.