Numerical solution of differential equations by radial basis function neural networks

Abstract

In this paper we present a method for solving linear ordinary differential equations (ODE) based on multiquadric (MQ) radial basis function networks (RBFNs). According to the thought of approximation of function and/or its derivatives by using radial basis function networks, another new RBFN approximation procedures different from are developed in this paper for solving ODE. This technique can determine all the parameters at the same time without a learning process. The advantage of this technique is that it doesn't need sufficient data, just relies on the domain and the boundary. Our results are more accurate.