On a nonlinear integro-differential equation of Fredholm type

Abstract

This work concerns an analytical and numerical study for a nonlinear Fredholm integro-differential equation, in this respect, we treat the conditions ensuring the existence and uniqueness of the solution for different varieties of kernels, thereafter, we construct a numerical approach based on the well known Nystrom method. The numerical examples illustrate the efficiency of the proposed method in connection with the existence and uniqueness conditions.