Universal approximation method for the solution of integral equations

Abstract

In this paper, we present a novel approach for approximating Hammerstein–Volterra delay integral equations (HVDIEs) by applying the universal approximation method through an artificial intelligence utility in a simple way. In this paper, neural network model (NNM) is applied as universal approximators for any nonlinear continuous functions. Here, neural network is considered as a part of large field called neural computing or soft computing. With this capability, the solution of Hammerstein–Volterra delay integral equation can be approximated by the appropriate NNM within an arbitrary accuracy.