GUDERMANNIAN NEURAL NETWORKS TO INVESTIGATE THE LIÉNARD DIFFERENTIAL MODEL

Abstract

The aim of this study is to present the numerical solutions of the Liénard nonlinear model by designing the structure of the computational Gudermannian neural networks (GNNs) along with the global/local search efficiencies of genetic algorithms (GAs) and interior-point algorithm (IPA), i.e. GNNs–GAs–IPA. A merit function in terms of differential system and its boundary conditions is designed and optimization is performed by using the proposed computational procedures of GAs–IPA to solve the Liénard nonlinear differential system. Three different highly nonlinear examples based on the Liénard differential system have been tested to check the competence, exactness and proficiency of the proposed computational paradigm of GNNs–GAs–IPA. The statistical performances in terms of different operators have been provided to check the reliability, consistency and stability of the computational GNNs–GAs–IPA. The plots of the absolute error, performance measures, results comparison, convergence analysis based on different operators, histograms and boxplots are also illustrated. Moreover, statistical gauges using minimum, mean, maximum, semi-interquartile range, standard deviation and median are also provided to authenticate the optimal performance of the GNNs–GAs–IPA.