Approximations of solutions of a class of neutral differential equations with a deviated argument

Abstract

In this paper, we study the approximations of solutions to a class of nonlinear neutral differential equations with a deviated argument in a Hilbert space. We consider an associated integral equation corresponding to the given problem and a sequence of approximate integral equations. We establish the existence and uniqueness of solutions to every approximate integral equation using the fixed point theory. Then, we prove the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. Next, we consider the Faedo-Galerkin approximations of solutions and prove some convergence results.