On Numerical Solution Approach for the Volterra-Fredholm Integral Equation

Abstract

In this paper, authors discussed the existence of a unique solution of Volterra-Fredholm integral equation of second kind in the space L p × C 0 T with a generalized kernel, in the domain of integration of several spaces, and t ∈ 0 T is the time is considered. A numerical technique used to obtain a system of Fredholm integral equations, Also authors considered the existence and the uniqueness of the system of equations. Moreover, the Toeplitz matrix method and Product Nystrom method are used to obtain numerically the solution of Fredholm integral equations with logarithmic kernel and Carleman function. Many special cases are considered and established from the work.