Extrapolation method of iterated collocation solution for two-dimensional nonlinear Volterra integral equations

摘要

In this paper, we study the numerical solution of two-dimensional nonlinear Volterra integral equation by collocation and iterated collocation method. Asymptotic error expansion of iterated collocation solution is obtained. Using Richardson's extrapolation, we show that the accuracy of numerical solution in the iterated collocation method can be improved greatly. Some numerical examples are given to illustrate this theory.