Resolution of differential equations with artificial neural networks: high gradients and arbitrary domains problems - DOI: 10.4025/actascitechnol.v27i1.1507

Abstract

In this paper, the ability of the multilayer perceptron neural network (MLP) in interpolation was used to analyze two classes of boundary value problems. The first class is formed by differential equations, with solutions which can have high gradients and the second are partial differential equations, defined on arbitrary shaped domain. Also, the methodologies proposed by Lagaris et al. (1998) were enlarged for differential equations subjected to Cauchy and mix boundary conditions type. The results of the artificial neural network method are very precise when comparison to the analytical ones or those of classical numerical methods to solve differential equations. The precision achieved in the results and the ability to handle the method, to solve those boundary value problems, were encouraging to keep the research, particularly on an important direction, concerning convergence and numerical stability