Browsing by Author "Sabir, Zulqurnain"

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Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge-Kutta Numerical Methods
(Hindawi Ltd, 2020) Sabir, Zulqurnain; Guirao, Juan L. G.; Saeed, Tareq; Erdogan, Fevzi
In this study, a novel second-order prediction differential model is designed, and numerical solutions of this novel model are presented using the integrated strength of the Adams and explicit Runge-Kutta schemes. The idea of the present study comes to the mind to see the importance of delay differential equations. For verification of the novel designed model, four different examples of the designed model are numerically solved by applying the Adams and explicit Runge-Kutta schemes. These obtained numerical results have been compared with the exact solutions of each example that indicate the performance and exactness of the designed model. Moreover, the results of the designed model have been presented numerically and graphically.
Design of Morlet Wavelet Neural Network for Solving a Class of Singular Pantograph Nonlinear Differential Models
(Ieee-inst Electrical Electronics Engineers inc, 2021) Nisar, Kashif; Sabir, Zulqurnain; Zahoor Raja, Muhammad Asif; Ag. Ibrahim, Ag. Asri; Erdogan, Fevzi; Haque, Muhammad Reazul; Rawat, Danda B.
The aim of this study is to design a layer structure of feed-forward artificial neural networks using the Morlet wavelet activation function for solving a class of pantograph differential Lane-Emden models. The Lane-Emden pantograph differential equation is one of the important kind of singular functional differential model. The numerical solutions of the singular pantograph differential model are presented by the approximation capability of the Morlet wavelet neural networks (MWNNs) accomplished with the strength of global and local search terminologies of genetic algorithm (GA) and interior-point algorithm (IPA), i.e., MWNN-GAIPA. Three different problems of the singular pantograph differential models have been numerically solved by using the optimization procedures of MWNN-GAIPA. The correctness of the designed MWNN-GAIPA is observed by comparing the obtained results with the exact solutions. The analysis for 3, 6 and 60 neurons are also presented to check the stability and performance of the designed scheme. Moreover, different statistical analysis using forty number of trials is presented to check the convergence and accuracy of the proposed MWNN-GAIPA scheme.
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.
A Stochastic Numerical Approach for a Class of Singular Singularly Perturbed System
(Public Library Science, 2022) Sabir, Zulqurnain; Botmart, Thongchai; Raja, Muhammad Asif Zahoor; Weera, Wajaree; Erdogan, Fevzi
In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO) and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An error-based fitness function is designed using the differential form of the SSP-BVPs and its boundary conditions. The optimization of this fitness function is performed by using the computing capabilities of ANNs-PSO-IPA. Four cases of two SSP systems are tested to confirm the performance of the suggested ANNs-PSO-IPA. The correctness of the scheme is observed by using the comparison of the proposed and the exact solutions. The performance indices through different statistical operators are also provided to solve the SSP-BVPs using the proposed ANNs-PSO-IPA. Moreover, the reliability of the scheme is observed by taking hundred independent executions and different statistical performances have been provided for solving the SSP-BVPs to check the convergence, robustness and accuracy.
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.