SOLVING PARTIAL DIFFERENTIAL EQUATIONS USING ARTICIFICAL NEURAL NETWORKS

Abstract

Partial differential equations have been widely applied in various fields of human knowledge, such as physics, chemistry, economics, image processing, etc. In this paper, we presented a method for solving the problem of partial differential equations (PDEs) with Dirichlet boundary conditions (This method) using single-hidden layer feedforward neural network (SLFN) called neural network method (NNM). The parameters of SLFNs are determined by training the neural network with backpropagation. The results show that NNM can obtain accuracy higher finite difference method.