Two-dimensional wavelets operational method for solving Volterra weakly singular partial integro-differential equations

Abstract

In this article, we discuss a method for finding an approximate solution of a class of two-dimensional linear Volterra weakly partial integro-differential equations. The operational matrices of integration, differentiation, and product are utilized to reduce the solution of the weakly partial integro-differential equation to the linear algebraic system of equations. Furthermore, some useful theorems are discussed to establish the convergence analysis of the proposed technique. Some numerical examples are solved by applying the presented scheme to show the effectiveness and applicability of the proposed scheme and also a comparison of error values between the two wavelets has been presented. Furthermore, some figures are plotted to demonstrate the error analysis of the proposed scheme.