Design of Mayer Wavelet Neural Networks for Solving Functional Nonlinear Singular Differential Equation

Abstract

In the present work, an advance computational intelligence paradigm based on functional Mayer artificial neural network (FM-ANN) is accessible for solving the singular nonlinear functional differential equation (NFDE) numerically. The solution of singular NFDE is performed by using the artificial neural networks (ANNs) optimized with global search genetic algorithm (GA) enhanced by local refinements of sequential quadratic (SQ) programming and the hybrid of GASQ programming. The proposed scheme is applied for solving three types of second-order singular NFDEs. In order to validate the correctness of the designed scheme, the comparison of the proposed and exact solutions has been performed. Moreover, the statistical interpretations are used to prove the worth, convergence, accuracy, stability, and robustness of FM-ANN-GASQP for the solution of singular NFDEs.