Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems


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 fuПоказать полностьюnction 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.

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Журнал: Numerical Analysis and Applications

Выпуск журнала: Vol. 13, Is. 1

Номера страниц: 34-44

ISSN журнала: 19954239


  • 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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