A neural network training algorithm for singular perturbation boundary value problems

A training algorithm for the Neural Network solution of Singular Perturbation Boundary Value Problems is presented. The solution is based on a single hidden layer feed forward Neural Network with a small number of neurons. The training algorithm adapts the training points grid so to be more tense in areas of the integration interval that solution has a layer or a peek. The algorithm automatically detects the areas of interest in the integration interval. The resulted Neural Network solutions are very accurate in a uniform way. The numerical tests in various test problems justify our arguments as the produced solutions prove to give smaller errors compare to their competitors.