A simple Taylor-series expansion method for a class of second kind integral equations

A simple yet effective Taylor-series expansion method is presented for a class of Fredholm integral equations of the second kind with smooth and weakly singular kernels. The equations studied in this paper arise in a number of applications, e.g., potential theory, radiative equilibrium, radiative heat transfer, and electrostatics. The approach leads to an approximate solution of the integral equation which can be expressed explicitly in a simple, closed form. The approximate solution is of sufficient accuracy as illustrated by the numerical examples arising from radiative heat transfer and electrostatics.