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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 2, Page 238
DOI: https://doi.org/10.7868/S0044466916020137
(Mi zvmmf10340)
 

This article is cited in 7 scientific papers (total in 7 papers)

Qualitatively stability of nonstandard 2-stage explicit Runge–Kutta methods of order two

M. M. Khalsaraei, F. Khodadosti

Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran
Full-text PDF (33 kB) Citations (7)
Abstract: When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Nonstandard finite differences (NSFDs) schemes can improve the accuracy and reduce computational costs of traditional finite difference schemes. In addition NSFDs produce numerical solutions which also exhibit essential properties of solution. In this paper, a class of nonstandard 2-stage Runge–Kutta methods of order two (we call it nonstandard RK2) is considered. The preservation of some qualitative properties by this class of methods are discussed. In order to illustrate our results, we provide some numerical examples.
Key words: ordinary differential equations, initial value problems, nonstandard Runge–Kutta methods, stability, elementary stable, positivity.
Received: 13.03.2014
Revised: 26.08.2014
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 2, Pages 235–242
DOI: https://doi.org/10.1134/S0965542516020123
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: English
Citation: M. M. Khalsaraei, F. Khodadosti, “Qualitatively stability of nonstandard 2-stage explicit Runge–Kutta methods of order two”, Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016), 238; Comput. Math. Math. Phys., 56:2 (2016), 235–242
Citation in format AMSBIB
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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