Bivariate Jacobi polynomials for solving Volterra partial integro-differential equations with the weakly singular kernel

Abstract

An operational matrix method is implemented based on the bivariate Jacobi polynomials to attain numerical solutions of a category of Volterra weakly singular partial integro-differential equations (VWSPI-DEs). Utilizing Jacobi approximations and their integral, derivative, and pseudo-integral operational matrices along with the collocation method reduces the given VWSPI-DE to a system of algebraic equations. Diverse forms of the Jacobi polynomials are used to investigate and compare errors of obtained approximate solutions. Moreover, some error bounds are computed for the error functions. Four experimental illustrations are solved to exhibit the effectiveness and suitability of the proposed scheme. © 2021 Elsevier B.V., All rights reserved.