Asymptotic stability of Runge–Kutta methods for nonlinear differential equations with piecewise continuous arguments

Liu, X.; Liu, M.Z.

doi:10.1016/j.cam.2014.11.059

Cited by 9 publications

(2 citation statements)

References 18 publications

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“…Liang et al considered numerical stability of system

u' (t) = L u (t) + M u ([t])

with matrix coefficients in the case of 2‐norm. The authors of presented stability analysis of the nonconfluent Runge‐Kutta methods applied to a nonlinear scalar EPCA. In , the asymptotical stability of the analytic and numerical solution with constant step‐size for a class of advanced linear impulsive EPCA were investigated.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Wang

2016

Numerical Methods Partial

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This article deals with the analytic and numerical stability of numerical methods for a parabolic partial differential equation with piecewise continuous arguments of alternately retarded and advanced type. First, application of the theory of separation of variables in matrix form and the Fourier method, the necessary and sufficient condition under which the analytic solution is asymptotically stable is derived. Then, the θ‐methods are applied to solve the corresponding initial value problem, the sufficient conditions for the asymptotic stability of numerical methods are obtained. Finally, several numerical examples are presented to support the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 531–545, 2017

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“…Liang et al considered numerical stability of system

u' (t) = L u (t) + M u ([t])

Section: Introductionmentioning

confidence: 99%

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Wang

2016

Numerical Methods Partial

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“…To solve the non-linear dynamics equation, the high efficiency and accuracy are considered. This paper combines finite difference method (FDM) and newton iterative method to solve the dynamics equation instead of traditional Runge-Kutta algorithm by which the operation is so complex and low-efficient to realize online [12]. And the proposed algorithm can be programmed in matlab and vc software.…”

Section: Introductionmentioning

confidence: 99%

Grasping Position Estimation for Prosthetic Hand

Wang¹,

Duan²,

Deng³

2015

Proceedings of the 2015 International Conference on Test, Measurement and Computational Methods

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For multi-freedom prosthetic hand, grasping stability is very important. Force closure method is often used to determine grasping force of each finger. The space position information must be obtained to compute grasping force by using this method. However, for prosthetic hand, the space position is hardly to get because angle sensors cannot be used. Thus dynamics model of tendon-driven prosthetic hand is built and solved by using the finite difference method and newton iteration algorithm base on the information of motor. Numerical simulation demonstrates that the method realizes the goal of calculating position approximately in real time and verifies the high efficiency and enough accuracy of the method.

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Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous arguments

Gurioli,

Wang,

Yan

2024

Numer Algor

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Asymptotic stability of Runge–Kutta methods for nonlinear differential equations with piecewise continuous arguments

Cited by 9 publications

References 18 publications

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Grasping Position Estimation for Prosthetic Hand

Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous arguments

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