Uniformly Convergent Numerical Method For Second Order Singularly Perturbed Fredholm Integro-Differential Equations

Abstract

In this thesis, a parameter-uniformly convergent numerical scheme is designed for solv ing linear second-order singularly perturbed Fredholm integro-differential equations. A parameter-uniform numerical method was constructed via the non-standard finite difference method to approximate the differential part and the composite Simpson’s 1/3 rule for the integral part. A convergence analysis has been carried out to show the parameter-uniform convergence of the proposed scheme. The maximum absolute errors and rate of convergence for different values of perturbation parameter ε and mesh sizes are tabulated for three model examples. The proposed scheme is shown to be second-order uniformly convergent.