Iterative method and convergence analysis for a kind of mixed nonlinear Volterra–Fredholm integral equation

摘要

In this paper, the iterative method is presented for numerically solving the nonlinear Volterra–Fredholm integral equation. First, considering some conditions on ki and λi (i=1,2) of the integral equation, then we define the equidistance collocation points and the integral part of equation is discretized by Newton–Cotes integration formula, finally, the approximate solutions of integral equation are obtain by iterative method. The convergence analysis of the integral equation is given. Some numerical examples are given to illustrate the accuracy and dependability of the method.