Modification artificial neural networks for solving singular perturbation problems

Abstract

In this paper, we introduce a modified method for solving singular perturbation problem for ordinary differential equations by using artificial neural networks. This modified method is called modified artificial neural network method (MANN). This new method is based on replacing each in the input vector training set) by a polynomial of first degree which will be as . Using MANN makes that training points should be selected over the open interval (a, b) without training the neural network in the range of first and end points. We illustrate this modified method by solving some numerical examples and provide a comparison between our results and those calculated by other numerical methods, this method demonstrates that neural networks produce solutions with good generalization and accuracy. Several examples are provided to demonstrate the suggested strategy.