A new operational approach for solving weakly singular integro–differential equations

Abstract

Based on Jacobi polynomials, an operational method is proposed tosolve weakly singular integro–differential equations. These equationsappear in various fields of science such as physics and engineering, themotion of a plate in a viscous fluid under the action of external forces,problems of heat transfer, and surface waves. To solve the weakly singularintegro–differential equations, a fast algorithm is used for simplifyingthe problem under study. The Laplace transform and Jacobi collocationmethods are merged, and thus, a novel approach is presented.Some theorems are given and established to theoretically support thecomputational simplifications which reduce costs. In order to show theefficiency and accuracy of the proposed method some numerical resultsare provided. It is found that the proposed method has lesser computationalsize compared to other common methods, such as Adomiandecomposition, Taylor expansion, and Bernstein operational methods.It is further found that the absolute errors are almost constant in thestudied interval.