Abstract:
This article explores the use of two orthogonal polynomial approximation methods to derive numerical solutions for boundary value problems involving higher-order fractional integro-differential equations. We introduce a perturbed collocation approach that transforms these perturbed equations into systems of algebraic equations by employing standard collocation points. The resulting algebraic systems are solved using Newton-Raphson's method, implemented through MAPLE 18 software. Several numerical examples are provided to demonstrate the accuracy and reliability of this method. The findings indicate that the proposed approach is both accurate and efficient. Additionally, the results show a favorable comparison with those obtained by Zhang et al. using the Homotopy Analysis Method.
Description:
Boundary value problems can be effectively approximated using simple and efficient numerical methods. Problems involving the wave equation, such as determining normal modes, are often formulated as boundary value problems. Sturm-Liouville problems represent an important class of boundary value problems, and their analysis involves the eigenfunctions of a differential operator, as discussed by Fu et al.
