Acta Mathematica Vietnamica

, Volume 44, Issue 4, pp 955–976 | Cite as

Stable Numerical Solution for a Class of Structured Differential-Algebraic Equations by Linear Multistep Methods

  • Vu Hoang LinhEmail author
  • Nguyen Duy Truong


It is known that when we apply a linear multistep method to differential-algebraic equations (DAEs), usually the strict stability of the second characteristic polynomial is required for the zero stability. In this paper, we revisit the use of linear multistep discretizations for a class of structured strangeness-free DAEs. Both explicit and implicit linear multistep schemes can be used as underlying methods. When being applied to an appropriately reformulated form of the DAEs, the methods have the same convergent order and the same stability property as applied to ordinary differential equations (ODEs). In addition, the strict stability of the second characteristic polynomial is no longer required. In particular, for a class of semi-linear DAEs, if the underlying linear multistep method is explicit, then the computational cost may be significantly reduced. Numerical experiments are given to confirm the advantages of the new discretization schemes.


Differential-algebraic equations Strangeness-free form Linear multistep methods Convergence Stability 

Mathematics Subject Classification (2010)

65L80 65L05 65L06 65L20 



The authors would like to thank the anonymous referee for the very helpful comments and suggestions that led to the improvements of this paper.

Funding Information

This work was supported by the Nafosted Project No. 101.02-2017.314.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics, Mechanics and InformaticsVietnam National UniversityThanh XuanVietnam
  2. 2.Tran Quoc Tuan UniversitySon TayVietnam

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