A Perturbed Orthogonal Collocation Approach for the Solution of Fredholm Integro-Differential Equations

Abstract

This paper considers the numerical solution of Fredholm integro-differential equations via a perturbed orthogonal collocation approach (POCA) with Chebyshev polynomials as trial functions. Here, the original problem is slightly perturbed by a perturbation term,^H_n(x) , in the form of a trial solution. The perturbed problem is then evaluated and solved by collocating at the zeros of the Chebyshev polynomials to generate an algebraic linear system of equations, which on solving via the Gaussian elimination method yields the unknown parameters, which generates the required approximate solution. Here, numerical evidence obtained via POCA was compared with the orthogonal collocation method (OCM) and exact solution as available in the literature. MAPLE 18 software was used for all computational frameworks in this research.