Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations \(y^{\prime \prime}(x) = f(x, y, y^\prime)\)
type: Item
instance of: scholarly article
title: Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations \(y^{\prime \prime}(x) = f(x, y, y^\prime)\)
zbMATH Open document ID: 1417.65137
DOI: 10.1155/2018/2393015
author: Tahani Salama Mohamed
author: Z. B. Ibrahim
author: Nik Mohd Asri Nik Long
author: N. Senu
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: This paper proposes and investigates a special class of explicit Runge-Kutta-Nyström (RKN) methods for problems in the form \(y''(x) = f(x, y, y')\) including third derivatives and denoted as STDRKN. The methods involve one evaluation of second derivative and many evaluations of third derivative per step. In this study, methods with two and three stages of orders four and five, respectively, are presented. The stability property of the methods is discussed. Numerical experiments have clearly shown the accuracy and the efficiency of the new methods.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 7026525
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2393015
OpenAlex ID: W2791096642
Wikidata QID: Q62630591
cites work: Q4875914
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description: scientific article; zbMATH DE number 7026525