Runge–Kutta Methods for Systems of Differential Equation with Piecewise Continuous Arguments: Convergence and Stability

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2017.1421554 ◽

2018 ◽

Vol 39 (7) ◽

pp. 784-799

Author(s):

Qi Wang ◽

Xiaoming Wang

Keyword(s):

Differential Equation ◽

Convergence And Stability ◽

Piecewise Continuous ◽

Runge Kutta ◽

Piecewise Continuous Arguments

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SYMMETRIC BIFURCATIONS IN A RING OF COUPLED DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411028489 ◽

2011 ◽

Vol 21 (02) ◽

pp. 431-436 ◽

Author(s):

BAODONG ZHENG ◽

JIAN MA ◽

HUIFENG ZHENG ◽

CHUNRUI ZHANG

Keyword(s):

Differential Equation ◽

Dihedral Group ◽

Equilibrium Points ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

Symmetry bifurcations of equilibrium points of three coupled differential equation with piecewise continuous arguments (EPCA) oscillators are studied. The system is equivariant under dihedral group D3 with order 6. This causes several types of symmetrical bifurcations.

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Stability analysis of Runge–Kutta methods for unbounded retarded differential equations with piecewise continuous arguments

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.12.008 ◽

2007 ◽

Vol 191 (1) ◽

pp. 57-66 ◽

Author(s):

M.Z. Liu ◽

S.F. Ma ◽

Z.W. Yang

Keyword(s):

Stability Analysis ◽

Differential Equations ◽

Piecewise Continuous ◽

Runge Kutta ◽

Piecewise Continuous Arguments ◽

Retarded Differential Equations

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Convergence and stability of the compensated split-step theta method for stochastic differential equations with piecewise continuous arguments driven by Poisson random measure

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.02.039 ◽

2018 ◽

Vol 340 ◽

pp. 296-317 ◽

Author(s):

Yulan Lu ◽

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Random Measure ◽

Poisson Random Measure ◽

Convergence And Stability ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

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Convergence and stability of stochastic theta method for nonlinear stochastic differential equations with piecewise continuous arguments

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113849 ◽

2021 ◽

pp. 113849

Author(s):

Yuhang Zhang ◽

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Nonlinear Stochastic Differential Equations ◽

Convergence And Stability ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

Stochastic Theta Method ◽

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

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2014.11.059 ◽

2015 ◽

Vol 280 ◽

pp. 265-274 ◽

Author(s):

X. Liu ◽

M.Z. Liu

Keyword(s):

Asymptotic Stability ◽

Differential Equations ◽

Nonlinear Differential Equations ◽

Piecewise Continuous ◽

Runge Kutta ◽

Piecewise Continuous Arguments

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Numerical oscillation and non-oscillation for differential equation with piecewise continuous arguments of mixed type

Applied Mathematics and Computation ◽

10.1016/j.amc.2016.11.031 ◽

2017 ◽

Vol 299 ◽

pp. 16-27 ◽

Author(s):

Jianfang Gao

Keyword(s):

Differential Equation ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments

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Stability analysis of Runge–Kutta methods for differential equations with piecewise continuous arguments of mixed type

International Journal of Computer Mathematics ◽

10.1080/00207160.2010.492425 ◽

2011 ◽

Vol 88 (5) ◽

pp. 1052-1066 ◽

Author(s):

Qi Wang ◽

Qingyong Zhu

Keyword(s):

Stability Analysis ◽

Differential Equations ◽

Piecewise Continuous ◽

Runge Kutta ◽

Piecewise Continuous Arguments

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Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments

Numerical Algorithms ◽

10.1007/s11075-020-00993-8 ◽

2020 ◽

Author(s):

Chengjian Zhang ◽

Xiaoqiang Yan

Keyword(s):

Differential Algebraic Equations ◽

Algebraic Equations ◽

Convergence And Stability ◽

Piecewise Continuous ◽

Piecewise Continuous Arguments ◽

Delay Differential ◽

Nonlinear Delay

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Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type

Journal of Inequalities and Applications ◽

10.1186/1029-242x-2012-290 ◽

2012 ◽

Vol 2012 (1) ◽

Author(s):

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Differential Equations ◽

Numerical Stability ◽

Piecewise Continuous ◽

Runge Kutta ◽

Piecewise Continuous Arguments

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Stability of Runge–Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2006.07.018 ◽

2007 ◽

Vol 54 (3) ◽

pp. 326-335 ◽

Author(s):

W.J. Lv ◽

Z.W. Yang ◽

M.Z. Liu

Keyword(s):

Differential Equations ◽

Piecewise Continuous ◽

Runge Kutta ◽

Piecewise Continuous Arguments ◽

Retarded Differential Equations

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