Abstract
In this manuscript, a new numerical approach is developed for approximating the solution of the one-dimensional and two-dimensional Volterra integro-differential equations (2D-VIDEs) of high-order. New operational matrices of integration, based on shifted Jacobi polynomials, are presented and used in combination with the collocation method to convert the 2D-VIDE into a system of algebraic equations. In addition, the convergence analysis of the suggested approach is investigated. The efficiency of the algorithm is demonstrated by means of several examples and the results are compared with those given using other numerical schemes.