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

Mufutau Ajani Rufai () and Higinio Ramos
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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

Mathematics, 2023, vol. 11, issue 6, 1-8

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.

Keywords: hybrid block technique; Lane–Emden–Fowler problems; optimization strategy; starting procedure; adaptive formulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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