Browsing by Author "Wahab, Hafiz Abdul"

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Intelligent Computing Technique for Solving Singular Multi-Pantograph Delay Differential Equation
(Springer, 2022) Sabir, Zulqurnain; Wahab, Hafiz Abdul; Nguyen, Tri Gia; Altamirano, Gilder Cieza; Erdogan, Fevzi; Ali, Mohamed R.
The purpose of this study is to introduce a stochastic computing solver for the multi-pantograph delay differential equation (MP-DDE). The MP-DDE is not easy to solve due to the singularities and pantograph terms. An advance computational intelligent paradigm is proposed to solve MP-DDE of the second kind by manipulating the procedures of the artificial neural networks (ANNs) through the optimization of genetic algorithm (GA) and sequential quadratic programming (SQP), i.e., ANNs-GA-SQP. A fitness function is constructed based on MP-DDE of second kind and corresponding boundary conditions. The correctness of the ANNs-GA-SQP is observed by performing the comparison of the proposed and exact solutions. The values of the absolute error (AE) in good measures are provided to solve the MP-DDE of the second kind. The efficacy and correctness of the stochastic computing approach to solve three problems of the MP-DDE of second kind to signify the efficiency, worth, and consistency. Moreover, the statistical soundings are applied to validate the accuracy and consistency.
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.
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.