Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation

• Published in: Mathematics and computers in simulation Vol. 172; pp. 1 - 14
• Main Authors: Sabir, Zulqurnain, Wahab, Hafiz Abdul, Umar, Muhammad, Sakar, Mehmet Giyas, Raja, Muhammad Asif Zahoor
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2020
• Subjects: Artificial neural networks; Genetic algorithm; Interior-point algorithm; Lane–Emden equation; Nonlinear; Singular; Lane–Emden equation; Singular; Interior-point algorithm; Nonlinear; Genetic algorithm; Artificial neural networks
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2020.01.005

In this study, a novel computational paradigm based on Morlet wavelet neural network (MWNN) optimized with integrated strength of genetic algorithm (GAs) and Interior-point algorithm (IPA) is presented for solving second order Lane–Emden equation (LEE). The solution of the LEE is performed by using modelling of the system with MWNNs aided with a hybrid combination of global search of GAs and an efficient local search of IPA. Three variants of the LEE have been numerically evaluated and their comparison with exact solutions demonstrates the correctness of the presented methodology. The statistical analyses are performed to establish the accuracy and convergence via the Theil’s inequality coefficient, mean absolute deviation, and Nash Sutcliffe efficiency based metrics. •The MWNN is designed successfully to solve the LEE.•Exploration in NNs to find the accurate and consistent results for the LEE.•The overlapping of the results established the correctness of the designed scheme.•Validation of the performance is checked through the statistical operators.•ANN is a good selection to solve complicated nonlinear models.