Numerical solution of second kind Fredholm integral equations system by using a Taylor-series expansion method

摘要

In this paper, we present a Taylor-series expansion method for a second kind Fredholm integral equations system with smooth or weakly singular kernels. This method reduce the system of integral equations to a linear system of ordinary differential equation. After constructing boundary conditions this system reduce to a system of equations that can be solved easily with any of the usual methods. Finally, we show the efficiency of the method using some numerical examples.