Comparative study of FeedForward and Radial Basis Function Neural Networks for solving an Environmental Boundary Value Problem

The aim of this paper is to introduce an alternative approach, using Neural Networks, for the approximate solution of a Boundary Value Problem (B.V.P) for second order quadratic Differential Equations, which arises in the numerical prediction of meteorological parameters. We used two different types of neural networks and more specific a FeedForward and a Radial Basis Function Neural Network, based on an approach which first presented by Lagari et al. (1998). Our objective is to examine whether the proposed methodology satisfies the solution system of differential equations of the second order, by studying the residual of the method for different time periods. Furthermore, we present a new, neural network, trial solution based on rational approximation, highlighting the advantages and disadvantages of each architecture. Finally, we study in terms of defect, the obtained results with those given by a previous work introduced by Famelis and Tsitouras 2015, in order to compare the new approach with classical schemes of numerical analysis.