Two Dimensional Fredholm Integral Equation with Time

Abstract

In this paper, the existence and uniqueness of solution of the twodimensional Fredholm integral equation with time, with singular kernel, arediscussed and proved. The Fredholm integral term (FIT) is considered inposition while the Volterra integral term (VIT) is considered in time. Usinga numerical technique we have a system of Fredholm integral equations(SFIEs) in two dimensions . This system of integral equations can be reducedto a linear algebraic system (LAS) of equations by using two differentmethods. These methods are: Toeplitz matrix method and Product Nystrommethod. A numerical examples are considered when the kernel takes thefollowing forms: Carleman function, logarithmic form, Cauchy kernel.