A Successive Numerical Scheme for Some Classes of Volterra-Fredholm Integral Equations

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms and imposes some conditions on the kernel of the integral equation to proved that the solution of the discretized form converges to the exact solution of the problem. Then the solution of the discretized form is approximated by an iterative scheme. Comparison of the approximate solution with exact solution shows that the our approach is easy and practical for some classes of linear and nonlinear Volterra-Fredholm integral equations.