Approximate solution of a class of linear integro-differential equations by Taylor expansion method

In this paper, a simple and effective Taylor expansion method is presented for solving a class of linear integro-differential equations including those of Fredholm and of Volterra types. By means of the nth-order Taylor expansion of an unknown function at an arbitrary point, a linear integro-differential equation can be converted approximately to a system of linear equations for the unknown function itself and its first n derivatives under initial conditions. The nth-order approximate solution is exact for a polynomial of degree equal to or less than n. Some examples are given to illustrate the accuracy of this method.