Franklin Wavelet Galerkin Method (FWGM) for Numerical Solution of Two-Dimensional Fredholm Integral Equations

Analytical solution of the two-dimensional integral equations are usually difficult. In many cases, approximate solutions are required. In this paper, we study the approximate solution for two-dimensional Fredholm integral equations of the first kind by two-dimensional wavelet. First, definition and the properties of one-dimensional Franklin wavelet must be presented. Next, integral equations converted via regularization method into the second kind, then, using the idea of wavelet Galerkin method, we will find an approximate solution. Finally, the convergence and efficiency of this method will be discussed with some examples which indicate the ability and accuracy of the method.