AN ALGORITHM FOR NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS USING HARMONY SEARCH AND NEURAL NETWORKS

Abstract

In this article, an algorithm based on artificial neural networks (ANN) and harmony search algorithm (HSA) is presented for the numerical solution of ordinary and partial differential equations. The power of ANN is used to construct an approximate solution of differential equations (DEs) such that it satisfies the DEs initial conditions (ICs) or boundary conditions (BCs) automatically. An automated design parameter selection approach is utilised to pick the optimum ANN ensemble from various combinations of ANN design parameters, random beginning weights, and biases. An unsupervised error is constructed in order to approximate the DE solution and HSA is used to minimize this error by training the neural network design parameters. A few test problems of various types are considered for verifying the algorithm's accuracy, convergence, and efficacy. The proposed algorithm is assessed using the results of statistical analysis obtained from a large number of independent runs for each model equation. The correctness and validity of the algorithm is also verified by comparing the obtained numerical results to the exact solution.