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numerical investigations to design a novel model based on the fifth order system of Emden–Fowler equations

Theoretical & Applied Mechanics Letters 2020年第5期10卷 333-342页

作者： Zulqurnain Sabir Mehmet Giyas Sakar Manshuk Yeskindirova Onur Saldir Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Mathematics Faculty of SciencesYuzuncu Yil UniversityVanTurkey Department of Translation Theory and Practice L.N.Gumilyov Eurasian National UniversityKazakhstan

The aim of the present study is to design a new fifth order system of Emden–Fowler equations and related four types of the *** standard second order form of the Emden–Fowler has been used to obtain the new *** shape factor that appear more than one time discussed in detail for every case of the designed *** singularity atη=0 at one point or multiple points is also discussed at each type of the *** validation and correctness of the new designed model,one example of each type based on system of fifth order Emden–Fowler equations are provided and numerical solutions of the designed equations of each type have been obtained by using variational iteration *** comparison of the exact results and present numerical outcomes for solving one problem of each type is presented to check the accuracy of the designed model.

关键词： Fifth order Emden-Fowler system Multiple singularity Shape factor numerical experimentations Variational iteration scheme

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Swarming Computational Efficiency to Solve a Novel Third-Order Delay Differential Emden-Fowler System

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Computers, Materials & Continua 2022年第12期73卷 4833-4849页

作者： Wajaree Weera Zulqurnain Sabir Muhammad Asif Zahoor Raja Sakda Noinang Thongchai Botmart Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Future Technology Research Center National Yunlin University of Science and Technology123 University RoadSection 3DouliouYunlin64002Taiwan Department of Mathematics Statistics and Computer Faculty of ScienceUbon Ratchathani UniversityUbon Ratchathani34190Thailand

The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks(ANNs)with the use of global search particle swarm optimization(PSO)along with the competent local search interior-point programming(IPP)called as *** proposed computational scheme is implemented for the numerical simulations of the third order nonlinear delay differential Emden-Fowler model(TON-DD-EFM).The TON-DD-EFM is based on two types along with the particulars of shape factor,delayed terms,and singular points.A merit function is performed using the optimization of PSOIPP to find the solutions to the *** effectiveness of the ANN-PSOIPP is certified through the comparison with the exact results for solving four examples of the *** scheme’s efficiency is observed by performing the absolute error in suitable measures found around 10−04 to 10−***,the statistical-based assessments for 100 trials are provided to compute the accuracy,stability,and constancy of the ANNPSOIPP for solving the TON-DD-EFM.

关键词： Third-order nonlinear emden-fowler system artificial neural network statistical results particle swarm optimization numerical experimentations local search programming

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