DOI 10.15507/2079-6900.24.202202.151-161

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 65L80

On the numerical solution of second-order stiff linear differential-algebraic equations

L. S. Solovarova1, T. D. Phuong2

1Matrosov Institute for System Dynamics and Control Theory of SB RAS (Irkutsk, Russian Federation)

2Institute of Mathematics of the Vietnamese Academy of Science and Technology (Hanoi, Vietnam)

Abstract. This article addresses systems of linear ordinary differential equations with an identically degenerate matrix in the main part. Such formulations of problems in literature are usually called differential-algebraic equations. In this work, attention is paid to the problems of the second order. Basing on the theory of matrix pencils and polynomials, sufficient conditions for existence and uniqueness of the equations’ solution are given. To solve them numerically, authors investigate a multistep method and its version based on a reformulated notation of the original problem. This representation makes it possible to construct methods whose coefficient matrices can be calculated at previous points. This approach has delivered good results in numerical solution of first-order differential-algebraic equations that contain stiff and rapidly oscillating components and have singular matrix pencil. The stability of proposed numerical algorithm is investigated for the well-known test equation. It is shown that this difference scheme has the first order of convergence. Numerical calculations of the model problem are presented.

Key Words: differential algebraic equations of the second order, stiff systems, difference schemes

For citation: L. S. Solovarova, T. D. Phuong. On the numerical solution of second-order stiff linear differential-algebraic equations. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 24:2(2022), 151–161. DOI: https://doi.org/10.15507/2079-6900.24.202202.151-161

Submitted: 27.03.2022; Revised: 26.04.2022; Accepted: 25.05.2022

Information about the authors:

Liubov S. Solovarova, Senior Researcher, Laboratory 1.1, Matrosov Institute for System Dynamics and Control Theory of SB RAS (134 Lermontova s., Irkutsk 664033, Russia), Ph.D. (Phys.-Math.), ORCID: http://orcid.org/0000-0002-3392-5232, soleilu@mail.ru

Ta D. Phuong, Associate Professor, Institute of Mathematics of the Vietnamese Academy of Science and Technology, (18 Hoang Quoc Viet Road, Hanoi 10307, Vietnam), ORCID: http://orcid.org/0000-0001-6955-1589, tdphuong@math.ac.vn

All authors have read and approved the final manuscript.

Conflict of interest: The authors declare no conflict of interest.

Creative Commons Attribution 4.0 International License This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License.