NUMERICAL SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS BY CROSSBRED NEURAL NETWORKS

Abstract

In this work, a novel numerical method based on crossbred neural network is proposed to solve the first order ordinary differential equation. Here crossbred neural network is considered as a part of large field called neural computing or soft computing. The crossbred feed forward neural network based on replacing each element in the training set by a polynomial of third degree. The model finds the approximated solution of the first order initial value problems inside its domain for the close enough neighborhood of the initial point. This method, in comparison with existing numerical methods, shows that the use of crossbred neural networks provides solutions with good generalization and high accuracy.

Keywords: first order ordinary differential equation, crossbred neural network, trial solution, minimized error function, hyperbolic tangent activation function