Mechanical algorithm for solving the second kind of Volterra integral equation

In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm for solving the second kind of Volterra integral equation is established, and a new Maple procedure voltproc is established, too. In particular, the algorithm can provide the exact solution of the second kind of Volterra integral equation by the methods of Neumann-series and mathematical induction, i.e., the algorithm also can computing the nth term by finite terms of the iterative kernel. Some examples are presented to illustrate the efficiency and accuracy of the algorithm. This will be useful for the integral equation solving and mathematical theorems automatic proving.