A mechanical algorithm for solving the Volterra integral equation

In this paper, by using the theories and methods of integral equation and computer algebra, a reliable algorithm for solving the Volterra integral equation is established, and a new Maple algorithm mainproc is established, too. Some examples are presented to illustrate the implementations of the algorithm. The results of the examples indicate that the algorithm of Taylor polynomial method is simple and effective, and can provide an accuracy approximate solution or exact solution of the Volterra integral equation and integro-differential equation. This will be useful for solving a system of integral equation or integro-differential equation.