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Solving SIVPs of Lane–Emden–Fowler Type Using a Pair of Optimized Nyström Methods with a Variable Step Size

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Listed:
  • Mufutau Ajani Rufai

    (Department of Mathematics, University of Bari Aldo Moro, 70125 Bari, Italy)

  • Higinio Ramos

    (Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
    Escuela Politécnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain)

Abstract

This research article introduces an efficient method for integrating Lane–Emden–Fowler equations of second-order singular initial value problems (SIVPs) using a pair of hybrid block methods with a variable step-size mode. The method pairs an optimized Nyström technique with a set of formulas applied at the initial step to circumvent the singularity at the beginning of the interval. The variable step-size formulation is implemented using an embedded-type approach, resulting in an efficient technique that outperforms its counterpart methods that used fixed step-size implementation. The numerical simulations confirm the better performance of the variable step-size implementation.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1535-:d:1103768
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    1. 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.
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