shifted jacobi collocation method for volterra- fredholm integral equation

in this paper, we compute the approximate numerical solution for the volterrafredholm integral equation (v-fie) by using the shifted jacobi collocation (sjc) method which depends on the operational matrices. some properties of the shifted jacobi polynomials are introduced. these properties allow us to transform the volterrafredholm integral equation into a system of algebraic equations in a nice form with the expansion coefficients of the solution. also, the convergence and error analysis are studied extensively. finally, some examples which verify the efficiency of the given method are supplied and compared with other methods.