Email this article On the numerical solution of second-order stiff linear differential-algebraic equations
- Authors: Solovarova L.S.1, Phuong T.D.2
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Affiliations:
- Matrosov Institute for System Dynamics and Control Theory of SB RAS
- Institute of Mathematics of the Vietnamese Academy of Science and Technology
- Issue: Vol 24, No 2 (2022)
- Pages: 151-161
- Section: Mathematics
- Published: 25.05.2022
- URL: https://ogarev-online.ru/2079-6900/article/view/364954
- DOI: https://doi.org/10.15507/2079-6900.24.202202.151-161
- ID: 364954
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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.
About the authors
Liubov S. Solovarova
Matrosov Institute for System Dynamics and Control Theory of SB RAS
Email: soleilu@mail.ru
ORCID iD: 0000-0002-3392-5232
Senior Researcher, Laboratory 1.1, Ph.D. (Phys.-Math.)
Russian Federation, 134 Lermontova s., Irkutsk 664033, RussiaTa D. Phuong
Institute of Mathematics of the Vietnamese Academy of Science and Technology
Author for correspondence.
Email: tdphuong@math.ac.vn
ORCID iD: 0000-0001-6955-1589
Associate Professor
Viet Nam, 18 Hoang Quoc Viet Road, Hanoi 10307, VietnamReferences
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