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Solving a System of Singular Perturbation Problems via Neural Networks

In this work, we will introduce a new procedure to solve a system of singular perturbation problems (SSPPs) via artificial neural networks. The neural networks use the code of back propagation with altered training algorithms such as quasi-Newton, Levenberg-Marquardt, and Bayesian regularization. In our research, we provide examples of two different types of systems, showing the accuracy, speed, resolution, and convergence of the new technology, the effectiveness of using the network techniques for solving this type of equations. The convergence properties of the technique and accuracy of the interpolation technique are considered.