Stability of Runge–Kutta methods in the numerical solution of linear impulsive differential equations

Liu, M.Z.; Liang, Hui; Yang, Zhanwen

doi:10.1016/j.amc.2007.03.044

Cited by 26 publications

(13 citation statements)

References 9 publications

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“…3) and classical 4-stage fourth order explicit Runge-Kutta methods (see Fig. 4) for (12) are asymptotically stable for h k = 1 m , k ∈ N, m is an arbitrary positive integer.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In recent years, the stability of numerical methods for IDEs has attracted more and more attention (see [11,12,15,17,22,29] etc.). Stability of Runge-Kutta methods with the constant stepsize for scalar linear IDEs has been studied by [17].…”

Section: Introductionmentioning

confidence: 99%

“…Stability of Runge-Kutta methods with the constant stepsize for scalar linear IDEs has been studied by [17]. Runge-Kutta methods with variable stepsizes for multidimensional linear IDEs has been investigated in [12]. Collocation methods for linear nonautonomous IDEs has been considered in [29].…”

Section: Introductionmentioning

confidence: 99%

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Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

Zhang

2020

Adv Differ Equ

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“…3) and classical 4-stage fourth order explicit Runge-Kutta methods (see Fig. 4) for (12) are asymptotically stable for h k = 1 m , k ∈ N, m is an arbitrary positive integer.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

Zhang

2020

Adv Differ Equ

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“…where β is defined in (19). The zero solution of the equation in (3) is asymptotically stable if and only if |λ M | < 1.…”

Section: Lemma 2 If the Coefficients A B And C Satisfymentioning

confidence: 99%

Stability of numerical solution for partial differential equations with piecewise constant arguments

Wang

2018

Adv Differ Equ

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In this paper, the numerical stability of a partial differential equation with piecewise constant arguments is considered. Firstly, the θ -methods are applied to approximate the original equation. Secondly, the numerical asymptotic stability conditions are given when the mesh ratio and the corresponding parameter satisfy certain conditions. Thirdly, the conditions under which the numerical stability region contains the analytic stability region are also established. Finally, some numerical examples are given to demonstrate the theoretical results. MSC: 65L07; 65L20

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“…Algorithmisation and implementation of numerical methods in programming language C++ was published in [6]. In [4] the issues of stability of numerical integration of linear differential equations by use of Runge-Kutta method is described. Methods of numerical integration Runge-Kutta of higher order and solution of differential equations by these methods were published in [8].…”

Section: Introductionmentioning

confidence: 99%

Application of Numerical Integration in Technical Practice

Rédl¹,

Váliková²,

Páleš³

et al. 2015

MERAA

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In this contribution we present the methodology of the solution of ordinary differential equation by the Runge -Kutta numerical method of fourth order. Analysed function is continuous and it has derivatives at every point. Records of the centre of the gravity velocities of agricultural technological vehicle are function values of the derivatives. Algorithm of numerical integration was implemented by the help of programming language C# in MS Visual Studio Pro 2010 developing environment. Trajectory of the centre of the gravity movement in three-dimensional space is the result of the listed algorithm.

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Stability of Runge–Kutta methods in the numerical solution of linear impulsive differential equations

Cited by 26 publications

References 9 publications

Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

Stability of numerical solution for partial differential equations with piecewise constant arguments

Application of Numerical Integration in Technical Practice

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