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Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation

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  • Sabir, Zulqurnain
  • Raja, Muhammad Asif Zahoor
  • Khalique, Chaudry Masood
  • Unlu, Canan

Abstract

In this paper, a neuro-evolution based numerical computing approach is presented for the solution of nonlinear third order multi-singular Emden–Fowler system of differential equations (MS-EF-SDEs) by manipulating the proficiency of continuous mapping through exploitation of feed-forward artificial neural networks (ANN). The weights or decision variables of these networks are optimized with genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., ANN-GA-SQP. An error based figure of merit is introduced using the differential model of MS EF-SDE along with corresponding boundary conditions. The objective/cost function is optimized by integrating capability of global and local search with GA and SQP, respectively. The competency of the designed ANN-GA-SQP approach in terms of significance, efficiency and consistency is perceived by solving MS-EF-SDEs. Moreover, statistical based investigations are implemented to validate the correctness of ANN-GA-SQP.

Suggested Citation

  • Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Khalique, Chaudry Masood & Unlu, Canan, 2021. "Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 799-812.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:799-812
    DOI: 10.1016/j.matcom.2021.02.004
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    References listed on IDEAS

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    1. Raheela Jamal & Baohui Men & Noor Habib Khan & Muhammad Asif Zahoor Raja, 2019. "Hybrid Bio-Inspired Computational Heuristic Paradigm for Integrated Load Dispatch Problems Involving Stochastic Wind," Energies, MDPI, vol. 12(13), pages 1-23, July.
    2. Pakdaman, M. & Ahmadian, A. & Effati, S. & Salahshour, S. & Baleanu, D., 2017. "Solving differential equations of fractional order using an optimization technique based on training artificial neural network," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 81-95.
    3. Ben Muatjetjeja & Chaudry Masood Khalique & Fazal Mahmood Mahomed, 2013. "Group Classification of a Generalized Lane-Emden System," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-12, February.
    4. Motlatsi Molati & Chaudry Masood Khalique, 2012. "Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, November.
    5. Shahid, Farah & Zameer, Aneela & Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2020. "A novel wavenets long short term memory paradigm for wind power prediction," Applied Energy, Elsevier, vol. 269(C).
    6. Daniel Mpho Nkwanazana & Ben Muatjetjeja & Chaudry Masood Khalique, 2013. "Conservation Laws for a Generalized Coupled Korteweg-de Vries System," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-5, July.
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    Cited by:

    1. Naz, Sidra & Raja, Muhammad Asif Zahoor & Kausar, Aneela & Zameer, Aneela & Mehmood, Ammara & Shoaib, Muhammad, 2022. "Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 88-113.
    2. Sabir, Zulqurnain & Said, Salem Ben & Baleanu, Dumitru, 2022. "Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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