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Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation

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  • Sabir, Zulqurnain
  • Saoud, Sahar
  • Raja, Muhammad Asif Zahoor
  • Wahab, Hafiz Abdul
  • Arbi, Adnène

Abstract

The present study presents numerical solution of the fourth order, singular, nonlinear Emden–Fowler equation integrated computational intelligence by exploiting the efficiency of feedforward artificial neural networks (ANNs), global optimization strength of genetic algorithms (GAs) and rapid local search of sequential quadratic programming (SQP). ANN is applied to discretize the nonlinear Emden–Fowler differential equation and consequentially construct a fitness/merit function on mean squared error sense. The optimization of the decision variables of ANN to solve the multi-singular, fourth order, nonlinear Emden–Fowler equation is performed by integrating capability GAs and SQP. The proficiency of the presented approach is certified on precision, convergence and stability indices, which are further enhanced through effectiveness, significance and reliability measures on statistical data for solving three different cases of the singular systems.

Suggested Citation

  • Sabir, Zulqurnain & Saoud, Sahar & Raja, Muhammad Asif Zahoor & Wahab, Hafiz Abdul & Arbi, Adnène, 2020. "Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 534-548.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:534-548
    DOI: 10.1016/j.matcom.2020.06.021
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    1. A. H. Bhrawy & A. S. Alofi & R. A. Van Gorder, 2014. "An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, May.
    2. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Sakar, Mehmet Giyas & Raja, Muhammad Asif Zahoor, 2020. "Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 1-14.
    3. 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).
    4. Edmund K Burke & Michel Gendreau & Matthew Hyde & Graham Kendall & Gabriela Ochoa & Ender Özcan & Rong Qu, 2013. "Hyper-heuristics: a survey of the state of the art," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(12), pages 1695-1724, December.
    5. Raja, Muhammad Asif Zahoor & Samar, Raza & Manzar, Muhammad Anwar & Shah, Syed Muslim, 2017. "Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 139-158.
    6. 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.
    7. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Erdoğan, Fevzi, 2019. "Stochastic numerical approach for solving second order nonlinear singular functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    Cited by:

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