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Browsing by Author "Umar, Muhammad"

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    Article
    Novel Design of Morlet Wavelet Neural Network for Solving Second Order Lane-Emden Equation
    (Elsevier, 2020) Sabir, Zulqurnain; Wahab, Hafiz Abdul; Umar, Muhammad; Sakar, Mehmet Giyas; Raja, Muhammad Asif Zahoor
    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. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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    Article
    Stochastic Numerical Approach for Solving Second Order Nonlinear Singular Functional Differential Equation
    (Elsevier Science inc, 2019) Sabir, Zulqurnain; Wahab, Hafiz Abdul; Umar, Muhammad; Erdogan, Fevzi
    A new computational intelligence numerical scheme is presented for the solution of second order nonlinear singular functional differential equations (FDEs) using artificial neural networks (ANNs), global operator genetic algorithms (GAs), efficient local operator interio-rpoint algorithm (IPA), and the hybrid combination of GA-IPA. An unsupervised error function is assembled for the DDE optimized by ANNs using the hybrid combination of GA-IPA. Three kinds of the second order nonlinear singular DDEs have been solved numerically and compared their results with the exact solutions to authenticate the performance and exactness of the present designed scheme. Moreover, statistical analysis based on Mean absolute deviation, Theil's inequality coefficient and Nash Sutcliffe efficiency is also performed to validate the convergence and accuracy of the present scheme. (C) 2019 Elsevier Inc. All rights reserved.