Тип публикации: статья из журнала
Год издания: 2020
Идентификатор DOI: 10.1134/S1995423920010036
Аннотация: ABSTRACT: A form of Rosenbrock-type methods optimal in terms of the number ofnon-zero parameters and computational costs per step is considered. Atechnique of obtaining (m, k) -methodsfrom some well-known Rosenbrock-type methods is justified. Formulas fortransforming the parameters of (m, k) -schemesand for obtaining a stability function are given for two canonicalrepresentations of the schemes. An L-stable(3 , 2) -methodof order 3 is proposed, which requires two evaluations of the function:one evaluation of the Jacobian matrix and oneLU-decompositionper step. A variable step size integration algorithm based on the(3 , 2) -methodis formulated. It provides a numerical solution for both explicit andimplicit systems of ODEs. Numerical results are presented to show theefficiency of the new algorithm. © 2020, Pleiades Publishing, Ltd.
Издание
Журнал: Numerical Analysis and Applications
Выпуск журнала: Vol. 13, Is. 1
Номера страниц: 34-44
ISSN журнала: 19954239
Персоны
- Levykin A.I. (Russian Acad Sci, Inst Computat Math & Math Geophys, Siberian Branch, Pr Akad Lavrenteva 6, Novosibirsk 630090, Russia; Novosibirsk State Univ, Ul Pirogova 2, Novosibirsk 630090, Russia)
- Novikov A.E. (Siberian Fed Univ, Pr Svobodnyi 79, Krasnoyarsk 660041, Russia)
- Novikov E.A. (Siberian Fed Univ, Pr Svobodnyi 79, Krasnoyarsk 660041, Russia; Russian Acad Sci, Siberian Branch, Inst Computat Modeling, Akademgorodok 50-44, Krasnoyarsk 660036, Russia)
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