Numerical Technique for solving Generalized Integro-differential-difference Equation with Variable Coefficient Combined Ultraspherical-Galerkin Method

Abstract

This study proposes a numerical technique for obtaining approximate solutions to generalized integro-differential-difference equations with variable coefficients using the Ultraspherical–Galerkin method. The method transforms the original equation into a system of algebraic equations. The approximate solution is expressed in terms of shifted ultraspherical polynomials. The stability and convergence of the proposed technique are analyzed. The accuracy and effectiveness of the method are further validated through several benchmark problems selected from the literature.