Delay-dependent stability of linear multistep methods for DAEs with multiple delays

Hu, Xiulin; Cong, Yuhao; Hu, Guang‐Da

doi:10.1007/s11075-017-0457-z

Cited by 7 publications

(2 citation statements)

References 27 publications

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“…In recent years, there has been extensively studied on the numerical stability and convergence of delay differential-algebraic equations [4][5][6][7][8][9][10][11][12][13][14][15]. Further, we can refer to [16][17][18][19] for details on the numerical stability and convergence of integral differential-algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations

Liu¹,

Zhang²,

Li³

et al. 2022

AAMM

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A novel canonical Euler splitting method is proposed for nonlinear composite stiff functional differential-algebraic equations, the stability and convergence of the method is evidenced, theoretical results are further confirmed by some numerical experiments. Especially, the numerical method and its theories can be applied to special cases, such as delay differential-algebraic equations and integral differential-algebraic equations.

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Section: Introductionmentioning

confidence: 99%

Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations

Liu¹,

Zhang²,

Li³

et al. 2022

AAMM

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“…Shifting and its consequences are studied in [1, 15, 26, 28-31, 51, 55]. Numerical time integration methods are developed and analyzed in [5,9,18,24,25,30,32,34,35,42,52,53]. Most of the references for the numerical methods require that there is no need to shift equations and that the associated DAE has differentiation index one.…”

Section: Introductionmentioning

confidence: 99%

Delay differential-algebraic equations in real-time dynamic substructuring

Unger

2020

Preprint

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Hybrid numerical-experimental testing is a standard approach for complex dynamical structures that are, on the one hand, not easy to model due to complexity and parameter uncertainty and, on the other hand, too expensive for full-scale experiments. The main idea is to subdivide the structure in a part that can be accurately simulated with numerical methods and an experimental component. The numerical simulation and the experiment are coupled in real-time by a so-called transfer system, which induces a time-delay into the system. In this paper, we study the solvability of the resulting hybrid numerical-experimental system, which is typically described by a set of nonlinear delay differential-algebraic equations, and extend existing results from the literature to this case.

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Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays

Kuang

et al. 2021

Calcolo

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Delay-dependent stability of linear multistep methods for DAEs with multiple delays

Cited by 7 publications

References 27 publications

Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations

Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations

Delay differential-algebraic equations in real-time dynamic substructuring

Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays

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