A Taylor expansion approach for solving integral equations

Abstract

We present an algebraic technique for solving integral equations. This technique is based on first differentiating both sides of the integral equation n times and then substituting the Taylor series for the unknown function in the resulting equation. This results in a linear algebraic system which can be solved approximately by a suitable truncation scheme. An interesting feature of this method is that we get exact solutions in many cases. We present four simple examples to illustrate this feature.