Shifted Jacobi collocation method for Volterra-Fredholm integral equation

Abstract

In this paper, we evaluate the approximate numerical solution for the Volterra-Fredholm integral equation (V-FIE) using the shifted Jacobi collocation (SJC) method. This method depends on the operational matrices. We present some properties of the shifted Jacobi polynomials. These properties together with the shifted Jacobi polynomials transform the Volterra-Fredholm integral equation into a system of algebraic equations in the expansion coefficients of the solution. We discuss the convergence and error analysis of the shifted Jacobi polynomials in detail. The efficiency of this method is verified through numerical examples and compared with others.