A New Block by Block Scheme via Quadrature Rule of Lobatto-Gaussian for Nonlinear Volterra Integral Equations

In this paper, a multistage technique called Block by Block technique is proposed to solve nonlinear Volterra integral equations by combining quadrature rule of Lobatto-Gaussian. This procedure gets automatically calculates several values of unknown functions at once and it is the most appropriate method which has the ability to show high accuracy for entire points of intervals, especially at the end points of large intervals. Also, the convergence of the presented method via the Gronwall inequality is proven and it is shown that the rate of convergence is at least O(h8). Some numerical experiments report the ability and accuracy of the proposed method.