Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients

Lv, Wanjin; Yang, Zhanwen; Liu, M.Z.

doi:10.1016/j.amc.2011.05.042

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…According to numerical stability theorem, 23,33 only if the eigenvalues of the coefficient matrix distribute in the stability domain of the explicit Euler method, the system will be convergent and stable. Considering the time-varying characteristic, an adaptive operator, ϕ i , is proposed in this paper to avoid the potential instability problems.…”

Section: Model Methods For Eclssmentioning

confidence: 99%

Numerical simulations of environment control and life support system in space station-oriented real-time system

Pang

2017

Proceedings of the Institution of Mechanical Engineers, Part G:

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An environment control and life support system (ECLSS) is an important system in a space station because it can provide a basic living environment for astronauts. The ECLSS is a typical time-variant complex system, hence there exits time-consuming technical difficulty during its development. The real-time simulation technology can help to accelerate its research process because some models of complex hardware need not to be built and calibrated at all. For a real-time simulation system with time-varying parameters, an implicit fixed time step numerical integration method is normally used as its solver. However, its computational efficiency is too low especially for the complex ECLSS simulation system on a single personal computer (PC) cluster. An explicit fixed time step integration method is computationally efficient, but their potential instability problems, which are caused by the time-varying parameters, limit its application to the ECLSS system. In this paper, an improved model method based on the explicit Euler method is proposed to simulate the complex time-variant ECLSS on a PC cluster. A simplified ECLSS system is established as an example to explain this proposed method. The eigenvalue estimation theory is used to analyze the numerical stability of the simplified system. Further, the potential instability problem of the explicit method can be avoided by an adaptive operator. Both of the stability and the accuracy of the proposed method are investigated carefully. It can be concluded from simulation results that this proposed method can provide a solution to realize the real-time simulation for the complex time-variant ECLSS on a PC cluster.

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Section: Model Methods For Eclssmentioning

confidence: 99%

Numerical simulations of environment control and life support system in space station-oriented real-time system

Pang

2017

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…Recently, Song and Liu [26] discussed the convergence of the linear multistep methods for EPCA with one delay [t] and constructed an improved linear multistep method. Lv et al [27] studied the analytical and numerical stability regions of Runge-Kutta methods for EPCA with complex coefficients. Moreover, The oscillations of θ-methods and Runge-Kutta methods were investigated in [28,29] for retarded EPCA, respectively.…”

Section: Introductionmentioning

confidence: 99%

Analytical and numerical stability of partial differential equations with piecewise constant arguments

Wang

Wen

2013

Numerical Methods Partial

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This article is concerned with the stability analysis of the analytic and numerical solutions of a partial differential equation with piecewise constant arguments of mixed type. First, by means of the similar technique in Wiener and Debnath [Int J Math Math Sci 15 (1992), 781–788], the sufficient conditions under which the analytic solutions asymptotically stable are obtained. Then, the θ‐methods are used to solve the above‐mentioned equation, the sufficient conditions for the asymptotic stability of numerical methods are derived. Finally, some numerical experiments are given to demonstrate the conclusions.Copyright © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1‐16, 2014

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Oscillation of numerical solution in the Runge-Kutta methods for equation x′(t) = ax(t) + a 0 x([t])

Wang

Shui-sheng²

2014

Acta Math. Appl. Sin. Engl. Ser.

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Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients

Cited by 7 publications

References 4 publications

Numerical simulations of environment control and life support system in space station-oriented real-time system

Numerical simulations of environment control and life support system in space station-oriented real-time system

Analytical and numerical stability of partial differential equations with piecewise constant arguments

Oscillation of numerical solution in the Runge-Kutta methods for equation x′(t) = ax(t) + a 0 x([t])

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