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

Standard

Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems. / Levykin, A. I.; Novikov, A. E.; Novikov, E. A.

In: Numerical Analysis and Applications, Vol. 13, No. 1, 25.02.2020, p. 34-44.

Research output: Contribution to journal › Article › peer-review

Harvard

Levykin, AI, Novikov, AE & Novikov, EA 2020, 'Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems', Numerical Analysis and Applications, vol. 13, no. 1, pp. 34-44. https://doi.org/10.1134/S1995423920010036

APA

Levykin, A. I., Novikov, A. E., & Novikov, E. A. (2020). Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems. Numerical Analysis and Applications, 13(1), 34-44. https://doi.org/10.1134/S1995423920010036

Vancouver

Levykin AI, Novikov AE, Novikov EA. Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems. Numerical Analysis and Applications. 2020 Feb 25;13(1):34-44. doi: 10.1134/S1995423920010036

Author

Levykin, A. I. ; Novikov, A. E. ; Novikov, E. A. / Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems. In: Numerical Analysis and Applications. 2020 ; Vol. 13, No. 1. pp. 34-44.

BibTeX

@article{2fa13acf904f4300a5ababa975dbb277,

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

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.",

author = "Levykin, {A. I.} and Novikov, {A. E.} and Novikov, {E. A.}",

year = "2020",

month = feb,

day = "25",

doi = "10.1134/S1995423920010036",

language = "English",

volume = "13",

pages = "34--44",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems

AU - Levykin, A. I.

AU - Novikov, A. E.

AU - Novikov, E. A.

PY - 2020/2/25

Y1 - 2020/2/25

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85080063468&partnerID=8YFLogxK

U2 - 10.1134/S1995423920010036

DO - 10.1134/S1995423920010036

M3 - Article

AN - SCOPUS:85080063468

VL - 13

SP - 34

EP - 44

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 1

ER -

ID: 23666119