ABSTRACT
This chapter utilizes the traditional multilayer artificial neural network (ANN) model for solving ordinary differential equations (ODEs). It considers a multilayer ANN model with one input layer containing a single node, a hidden layer with m nodes, and one output node. The ANN trial solution of the differential equation is a sum of two terms. The first term satisfies the initial or boundary conditions, while the second term contains the output of the ANN with adjustable parameters. The chapter reviews the utilization of the feed-forward neural network model and unsupervised error back-propagation algorithm, and explains how to modify of network parameters without the use of any optimization technique. It provides examples considering first-order linear ODE, second-order differential equation with initial conditions that describes a model of an undamped free vibration spring mass system and a system of coupled first-order ODEs.
