Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method

In this paper, we present a Taylor-series expansion method for a class of Volterra integral equations of second kind with smooth or weakly singular kernels. This method use Taylor-series approximation method for integral equation and transform the integral equation to an nth order, linear differential equation. Boundary conditions for differential equation produce in easy way. This method gives an approximate simple and closed form solution for integral equation. Some numerical example use to illustrate the accuracy of method.