Solving ordinary and partial differential equation using Legendre neural network DDY2 method

In this paper, we present a new method based on modification on single layer Legendre Neural Network(LeNN) method to be Legendre Neural Network DDY2 (LeNNDDY2) method to solve ordinary and partial differential equation. The activation function on the hidden layer is changed by Legendre polynomial expansion. The optimization method used in weight and bias updates is the DDY2 conjugate gradient method. For example problems, the numerical results have been compared with the other methods and gotten better results. © 2021, International Association of Engineers. All rights reserved.