A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem

Abstract

We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rules, exponential basis functions and remainder terms in integral form. We show that this method is the first order convergent in the discrete maximum norm for original problem (independent of the perturbation parameter ε). To illustrate the theoretical results, we solve test problem and we also give the error distributions in the solution in Table 1 and Figures 1-3.

A New Numerical Scheme for Singularly Perturbed Reaction-Diffusion Problems

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

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