Exponentially fitted finite difference method for singularly perturbed Fredholm integero-differential equations

Abstract

In this thesis, we developed an ε uniform convergent scheme for solving singularly perturbed linear second order Fredholm integro differential equation. A parameter-uniform numerical method was constructed using exponentially fitted finite difference method to approximate the differential part and the composite Simpson’s 1/3 rule for the integral part. The schemes stability and convergence analysis has been carried out . The maximum absolute errors and rate of convergence is tabulated for different values of perturbation parameter ε and mesh sizes using different numerical test examples.