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An adaptive pair of one-step hybrid block Nyström methods for singular initial-value problems of Lane–Emden–Fowler type

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  • Ramos, Higinio
  • Rufai, Mufutau Ajani

Abstract

In this paper, an optimized pair of hybrid block techniques is presented and successfully applied to integrate second-order singular initial value problems of Lane–Emden–Fowler type emanating from applied sciences and engineering. An adaptive technique implementation is considered. One of the proposed one-step hybrid block techniques is obtained by using three intermediate points. The obtained block formulas are then paired with a suitable set of formulas applied at the first step to avoid the singularity issue at the left end of the integration interval. Some real-world application problems, including the well-known isothermal gas sphere’s equations, are integrated numerically to ascertain our developed error estimation and control strategy impact. The presented numerical simulations confirm the superiority and robust performance of the proposed scheme.

Suggested Citation

  • Ramos, Higinio & Rufai, Mufutau Ajani, 2022. "An adaptive pair of one-step hybrid block Nyström methods for singular initial-value problems of Lane–Emden–Fowler type," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 497-508.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:497-508
    DOI: 10.1016/j.matcom.2021.10.023
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    References listed on IDEAS

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    1. Roul, Pradip & Prasad Goura, V.M.K. & Agarwal, Ravi, 2019. "A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 283-304.
    2. Roul, Pradip & Prasad Goura, V.M.K., 2019. "B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 428-450.
    3. Singh, Randhir & Guleria, Vandana & Singh, Mehakpreet, 2020. "Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 123-133.
    4. Liu, Chein-Shan & El-Zahar, Essam R. & Chang, Chih-Wen, 2021. "A boundary shape function iterative method for solving nonlinear singular boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 614-629.
    5. Goura, V.M.K. Prasad & Roul, Pradip, 2019. "Erratum to: B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 198-201.
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    Cited by:

    1. Mufutau Ajani Rufai & Higinio Ramos, 2023. "Solving SIVPs of Lane–Emden–Fowler Type Using a Pair of Optimized Nyström Methods with a Variable Step Size," Mathematics, MDPI, vol. 11(6), pages 1-8, March.

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