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## Liu, Mingzhu

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 Author ID: liu.mingzhu Published as: Liu, M.; Liu, M. Z.; Liu, Ming Zhu; Liu, Ming-Zhu; Liu, MingZhu; Liu, Mingzhu
 Documents Indexed: 147 Publications since 1987
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#### Co-Authors

 0 single-authored 21 Song, Minghui 13 Ding, Xiaohua 10 Zhao, Jingjun 9 Hu, Guangda 9 Xu, Yang 7 Li, Dongsong 7 Liang, Hui 7 Yang, Zhanwen 5 Fan, Zhencheng 5 Zhao, Guihua 4 Cao, Wanrong 4 Gao, Jianfang 4 Lv, Wanjin 4 Wang, Qiubao 3 Jaffer, Syed Khalid 3 Jin, Chengri 3 Liu, Xing 3 Lu, Chun 3 Qiu, Shenshan 3 Sidibe, Birama Sory 3 Zhang, Chunrui 3 Zhang, Guilai 3 Zheng, Baodong 2 Chu, Zhongwu 2 Liang, Jiuzhen 2 Lu, Yulan 2 Ma, Shufang 2 Mao, Xuerong 2 Wu, Kaining 2 Zou, Jinying 1 An, Dawen 1 Bai, Hong 1 Dai, Hongyu 1 Fan, Dejun 1 Fang, Zhencheng 1 Gong, Yunye 1 Guo, Changyong 1 Han, Dedong 1 Hu, Guangdi 1 Lu, Wanjin 1 Su, Huan 1 Wang, Qi 1 Wang, Xiaobiao 1 Xiao, Yu 1 Yang, Huizi 1 Yu, Zhanhua 1 Zheng, Hongzhen 1 Zhu, Qingyong
all top 5

#### Serials

 18 Applied Mathematics and Computation 17 Journal of Natural Science of Heilongjiang University 11 Journal of Harbin Institute of Technology 7 Journal of Computational and Applied Mathematics 7 Journal of Computational Mathematics 7 Journal of Harbin Institute of Technology. New Series 3 Chaos, Solitons and Fractals 3 Numerical Mathematics 3 International Journal of Computer Mathematics 2 Computers & Mathematics with Applications 2 Journal of Mathematical Analysis and Applications 2 Applied Numerical Mathematics 2 Abstract and Applied Analysis 2 Discrete Dynamics in Nature and Society 1 BIT 1 IEEE Transactions on Automatic Control 1 Systems & Control Letters 1 IMA Journal of Mathematical Control and Information 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Mathematica Applicata 1 IEEE Transactions on Signal Processing 1 Linear Algebra and its Applications 1 Numerical Mathematics 1 Journal of Inequalities and Applications 1 Nonlinear Analysis. Real World Applications 1 Mathematical Modelling and Analysis 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Applied Mathematics and Computing 1 Chinese Journal of Computational Mechanics 1 Advances in Difference Equations 1 International Journal of Numerical Analysis and Modeling
all top 5

#### Fields

 83 Numerical analysis (65-XX) 82 Ordinary differential equations (34-XX) 20 Probability theory and stochastic processes (60-XX) 6 Biology and other natural sciences (92-XX) 5 Partial differential equations (35-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Systems theory; control (93-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Difference and functional equations (39-XX) 1 Integral equations (45-XX)

#### Citations contained in zbMATH

100 Publications have been cited 1,055 times in 596 Documents Cited by Year
The stability of the $$\theta$$-methods in the numerical solution of delay differential equations. Zbl 0693.65056
Liu, M. Z.; Spijker, M. N.
1990
Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. Zbl 1059.65006
Liu, Mingzhu; Cao, Wanrong; Fan, Zhencheng
2004
Properties of analytic solution and numerical solution of multi-pantograph equation. Zbl 1059.65060
Liu, M. Z.; Li, Dongsong
2004
Stability of $$\theta$$-methods for advanced differential equations with piecewise continuous arguments. Zbl 1082.65078
Song, M. H.; Yang, Z. W.; Liu, M. Z.
2005
Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations. Zbl 1107.60030
Fan, Zhencheng; Liu, Mingzhu; Cao, Wanrong
2007
MS-stability of the Euler–Maruyama method for stochastic differential delay equations. Zbl 1074.65007
Cao, Wanrong; Liu, Mingzhu; Fan, Zhencheng
2004
Stability of Runge–Kutta methods in the numerical solution of equation $$u'(t)=au(t)+a_{0}u([t])$$. Zbl 1052.65070
Liu, M. Z.; Song, M. H.; Yang, Z. W.
2004
Periodic solutions for a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay. Zbl 1152.34046
Ding, Xiaohua; Lu, Chun; Liu, Mingzhu
2008
The $$\alpha$$th moment stability for the stochastic pantograph equation. Zbl 1206.65021
Fan, Zhencheng; Song, Minghui; Liu, Mingzhu
2009
Preservation of oscillations of the Runge-Kutta method for equation $$x'(t)+ax(t)+a_1x([t - 1])=0$$. Zbl 1189.65143
Liu, M. Z.; Gao, J. F.; Yang, Z. W.
2009
Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system. Zbl 1083.65129
Zhao, J. J.; Xu, Y.; Liu, M. Z.
2005
Stability of Runge-Kutta methods in the numerical solution of equation $$u'(t)=au(t)+a_{0} u([t])+a_{1} u([t-1])$$. Zbl 1063.65070
Yang, Zhanwen; Liu, Mingzhu; Song, Minghui
2005
Stability of $$\theta$$-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments. Zbl 1209.65091
Liang, Hui; Liu, M. Z.; Lv, Wanjin
2010
The Euler scheme and its convergence for impulsive delay differential equations. Zbl 1202.65088
Ding, Xiaohua; Wu, Kaining; Liu, Mingzhu
2010
Oscillation analysis of numerical solution in the $$\theta$$-methods for equation $$x\prime (t) + ax(t) + a_{1}x([t - 1]) = 0$$. Zbl 1118.65080
Liu, M. Z.; Gao, Jianfang; Yang, Z. W.
2007
Stability of Runge-Kutta methods in the numerical solution of linear impulsive differential equations. Zbl 1193.65121
Liu, M. Z.; Liang, Hui; Yang, Z. W.
2007
Hopf bifurcation in numerical approximation of a class delay differential equations. Zbl 1037.34068
Zhang, Chunrui; Liu, Mingzhu; Zheng, Baodong
2003
Numerical methods for impulsive differential equation. Zbl 1145.65317
Ran, X. J.; Liu, M. Z.; Zhu, Q. Y.
2008
Asymptotical stability of numerical methods with constant stepsize for pantograph equations. Zbl 1095.65075
Liu, M. Z.; Yang, Z. W.; Hu, G. D.
2005
Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type. Zbl 1207.65103
Wang, Qi; Zhu, Qingyong; Liu, Mingzhu
2011
Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations. Zbl 1323.34085
Zhang, G. L.; Song, M. H.; Liu, M. Z.
2015
Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments. Zbl 1193.65122
Liu, M. Z.; Ma, S. F.; Yang, Z. W.
2007
The weighted logarithmic matrix norm and bounds of the matrix exponential. Zbl 1060.15024
Hu, Guang-Da; Liu, Mingzhu
2004
Quantification of mixing in aperiodic chaotic flows. Zbl 0823.76020
Liu, M.; Muzzio, F. J.; Peskin, R. L.
1994
Noise suppresses exponential growth under regime switching. Zbl 1173.60024
Hu, Guangda; Liu, Mingzhu; Mao, Xuerong; Song, Minghui
2009
Runge-Kutta methods for the multi-pantograph delay equation. Zbl 1070.65060
Li, D.; Liu, M. Z.
2005
Stability of the analytic and numerical solutions for impulsive differential equations. Zbl 1233.65044
Liang, Hui; Song, M. H.; Liu, M. Z.
2011
Stability criteria of linear neutral systems with multiple delays. Zbl 1366.34098
Hu, Guang-Da; Liu, Mingzhu
2007
Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. Zbl 1115.65007
Ding, Xiaohua; Wu, Kaining; Liu, Mingzhu
2006
Stability of a class of Runge–Kutta methods for a family of pantograph equations of neutral type. Zbl 1168.65371
Zhao, J. J.; Xu, Y.; Wang, H. X.; Liu, M. Z.
2006
The stability of modified Runge-Kutta methods for the pantograph equation. Zbl 1094.65075
Liu, M. Z.; Yang, Z. W.; Xu, Y.
2006
$$H_{\alpha}$$-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations. Zbl 1125.65076
Ma, S. F.; Yang, Z. W.; Liu, M. Z.
2007
Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments. Zbl 1175.65088
Lv, W. J.; Yang, Z. W.; Liu, M. Z.
2007
Strong convergence of the partially truncated Euler-Maruyama method for a class of stochastic differential delay equations. Zbl 1444.34099
Zhang, Wei; Song, M. H.; Liu, M. Z.
2018
Noise expresses exponential growth under regime switching. Zbl 1184.93027
Hu, Guangda; Liu, Mingzhu; Mao, Xuerong; Song, Minghui
2009
A new modification of Adomian decomposition method for solving a kind of evolution equation. Zbl 1121.65355
Jin, Chengri; Liu, Mingzhu
2005
On the solvability of the systems of equations arising in implicit Runge- Kutta methods. Zbl 0661.65078
Liu, M. Z.; Kraaijevanger, J. F. B. M.
1988
Stability analysis of Runge-Kutta methods for systems $$u'(t)=Lu(t)+Mu([t])$$. Zbl 1364.65144
Liang, Hui; Liu, M. Z.; Yang, Z. W.
2014
Asymptotic stability of a class of impulsive delay differential equations. Zbl 1255.34079
Zhang, G. L.; Song, M. H.; Liu, M. Z.
2012
Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics. Zbl 1237.65064
Gao, Jianfang; Song, Minghui; Liu, Mingzhu
2011
Convergence and stability of the semi-implicit Euler method with variable stepsize for a linear stochastic pantograph differential equation. Zbl 1214.65003
Xiao, Yu; Song, Minghui; Liu, Mingzhu
2011
Exponential stability of Euler-Maruyama solutions for impulsive stochastic differential equations with delay. Zbl 1229.65031
Zhao, Guihua; Song, M. H.; Liu, M. Z.
2010
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations. Zbl 1198.65108
Wang, Qiubao; Li, Dongsong; Liu, M. Z.
2009
Numerical Hopf bifurcation of linear multistep methods for a class of delay differential equations. Zbl 1161.65056
Liu, M. Z.; Wang, Qiubao
2009
Stability and bifurcation of a numerical discretization Mackey-Glass system. Zbl 1132.37030
Ding, Xiaohua; Fan, Dejun; Liu, Mingzhu
2007
$$\mathcal H$$-stability of Runge-Kutta methods with general variable stepsize for pantograph equation. Zbl 1038.65070
Xu, Yang; Liu, Mingzhu
2004
Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading. Zbl 1038.74613
Liu, M.; Hsia, K. J.
2003
Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients. Zbl 1252.65133
Lv, W. J.; Yang, Z. W.; Liu, M. Z.
2011
Convergence and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Zbl 1376.60066
Lu, Y. L.; Song, M. H.; Liu, M. Z.
2017
Linear multistep methods for impulsive differential equations. Zbl 1248.65076
Liu, Xing; Song, M. H.; Liu, M. Z.
2012
Almost surely asymptotic stability of numerical solutions for neutral stochastic delay differential equations. Zbl 1252.65018
Yu, Zhanhua; Liu, Mingzhu
2011
Extinction and permanence of the numerical solution of a two-prey one-predator system with impulsive effect. Zbl 1218.65071
Liang, Hui; Liu, Mingzhu; Song, Minghui
2011
Exact solution properties of a multi-pantograph delay differential equation. Zbl 1087.34536
Li, Dongsong; Liu, Mingzhu
2000
Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments. Zbl 1309.65084
Liu, Xing; Liu, Ming-Zhu
2015
Analytic and numerical exponential asymptotic stability of nonlinear impulsive differential equations. Zbl 1291.65237
Liu, Xing; Zhang, G. L.; Liu, M. Z.
2014
Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. Zbl 1180.65094
Yang, Z. W.; Liu, M. Z.; Nieto, Juan J.
2009
Stability of Runge-Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments. Zbl 1140.65057
Lv, W. J.; Yang, Z. W.; Liu, M. Z.
2007
Stability of the Rosenbrock methods for the neutral delay differential-algebraic equations. Zbl 1081.65079
Zhao, J. J.; Xu, Y.; Dong, S. Y.; Liu, M. Z.
2005
Suitability of Runge-Kutta methods. Zbl 0628.65050
Liu, M. Z.; Dekker, K.; Spijker, M. N.
1987
Calabi-Yau properties of nontrivial Noetherian DG down-up algebras. Zbl 1410.16016
Mao, X.-F.; He, J.-W.; Liu, M.; Xie, J.-F.
2018
Exponential stability of impulsive delay differential equations. Zbl 1302.34110
Zhang, G. L.; Song, Ming Hui; Liu, Ming Zhu
2013
Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type. Zbl 1280.65070
Song, Minghui; Liu, Mingzhu
2012
Stability and Neimark-Sacker bifurcation in Runge-Kutta methods for a predator-prey system. Zbl 1190.65116
Wang, Qiubao; Liu, M. Z.
2009
Input-to-state stability of Runge-Kutta methods for nonlinear control systems. Zbl 1114.93090
Hu, Guang-Da; Liu, Mingzhu
2007
Global exponential stability analysis for neutral delay-differential systems: an LMI approach. Zbl 1137.34353
Liu, M.
2006
Simple criteria for stability of two-dimensional linear systems. Zbl 1370.93161
Hu, Guang-Da; Liu, Mingzhu
2005
Asymptotic stability of Runge-Kutta methods for the pantograph equations. Zbl 1065.65102
Zhao, Jingjun; Cao, Wanrong; Liu, Mingzhu
2004
Asymptotic stability for Gauss methods for neutral delay differential equations. Zbl 1002.65087
Sidibe, Birama Sory; Liu, Mingzhu
2002
Asymptotic stability of numerical solutions to pantograph delay differential equations. Zbl 0970.65548
Li, Dongsong; Liu, Mingzhu
1999
Stability of numerical solutions to pantograph delay systems. Zbl 0970.65550
Liang, Jiuzhen; Liu, Mingzhu
1996
The stability of $$\theta$$-methods for pantograph delay differential equations. Zbl 0869.65052
Liang, Jiuzhen; Qiu, Shenshan; Liu, Mingzhu
1996
Effects of manifolds and corner singularities on stretching in chaotic cavity flows. Zbl 0816.76026
Liu, M.; Muzzio, F. J.; Peskin, R. L.
1994
Convergence and stability of impulsive stochastic differential equations. Zbl 1391.93285
Song, M. H.; Yang, H. Z.; Liu, M. Z.
2017
Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations. Zbl 1338.34133
Zhang, G. L.; Song, Minghui; Liu, M. Z.
2015
Stability of analytic and numerical solutions for differential equations with piecewise continuous arguments. Zbl 1244.34097
Song, Minghui; Liu, M. Z.
2012
Mean square stability of stochastic differential equations with piecewise continuous arguments. Zbl 1199.60205
Dai, Hongyu; Liu, Mingzhu
2008
Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback. Zbl 1138.93030
Ding, Xiaohua; Su, Huan; Liu, Mingzhu
2008
The asymptotically mean square stability of the linear stochastic pantograph equation. Zbl 1141.60350
Fan, Zhencheng; Liu, Mingzhu
2007
$${\mathcal H}$$-stability of Runge-Kutta methods with variable stepsize for system of pantograph equations. Zbl 1059.65068
Xu, Yang; Zhao, Jingjun; Liu, Mingzhu
2004
Delay-dependent treatment of linear multistep methods for neutral delay differential equations. Zbl 1059.65062
Jaffer, Syed Khalid; Liu, Mingzhu
2003
Estimation of numerically stable step-size for neutral delay-differential equations via spectral radius. Zbl 0868.65054
Hu, Guang-Di; Hu, Guang-Da; Liu, Mingzhu
1997
Three-dimensional infinite boundary elements for contact problems. Zbl 0789.73078
Liu, M.; Farris, T. N.
1993
Numerical stability and oscillation of the Runge-Kutta methods for equation $$x'(t)=ax(t)+a_0x(M[\frac{t+N}{M}])$$. Zbl 1416.65210
Song, Minghui; Liu, M. Z.
2012
Finite size effects and symmetry breaking in the evolution of networks of competing Boolean nodes. Zbl 1211.37036
Liu, M.; Bassler, K. E.
2011
Numerical simulation of periodic solutions for a class of numerical discretization neural networks. Zbl 1201.34108
Lu, Chun; Ding, Xiaohua; Liu, Mingzhu
2010
Exponential $$p$$-stability of impulsive stochastic differential equations with delays. Zbl 1224.60154
Zhao, Guihua; Liu, Mingzhu; Lü, Wanjin
2009
Properties of the weighted logarithmic matrix norms. Zbl 1144.15018
Hu, Guang-Da; Liu, Mingzhu
2008
Hopf bifurcation in numerical approximation for delay differential equations. Zbl 1042.65055
Zhang, Chunrui; Liu, Mingzhu; Zheng, Baodong
2003
Delay-dependent stability analysis of Runge-Kutta methods for neutral delay differential equations. Zbl 1067.65083
Sidibe, B. S.; Song, Minghui; Liu, Mingzhu
2002
Convergence aspects of step-parallel iteration of Runge-Kutta methods for delay differential equations. Zbl 1020.65041
Ding, Xiaohua; Liu, Mingzhu
2002
Criterion for decoupling dynamic equations of motion of linear gyroscopic systems. Zbl 0799.70010
Liu, M.; Wilson, J. M.
1992
Convergence rate of the truncated Milstein method of stochastic differential delay equations. Zbl 1429.65026
Zhang, Wei; Yin, Xunbo; Song, M. H.; Liu, M. Z.
2019
Convergence and stability of the compensated split-step theta method for stochastic differential equations with piecewise continuous arguments driven by Poisson random measure. Zbl 1391.60166
Lu, Yulan; Song, Minghui; Liu, Mingzhu
2018
New iterative method based on Laplace decomposition algorithm. Zbl 1266.65119
Widatalla, Sabir; Liu, M. Z.
2013
Stability of the semi-implicit Euler method for a linear impulsive stochastic differential equation. Zbl 1211.65008
Liu, Mingzhu; Zhao, Guihua; Song, Minghui
2011
$$P$$-stability of continuous Runge-Kutta-Nyström method for a class of delayed second order differential equation. Zbl 1095.65073
Ding, Xiaohua; Zou, Jinying; Liu, Mingzhu
2005
Analysis and experimental verification of the linear correlation of the operation condition among the bifurcation points of current-mode-controlled buck-boost converter. Zbl 1061.94553
Cheng, K. W. Eric; Liu, M.
2005
Asymptotic stability properties of $$\theta$$-methods for the multi-pantograph delay differential equation. Zbl 1054.65081
Li, Dongsong; Liu, Mingzhu
2004
A numerical method for study of the unsteady viscous flow between two concentric rotating spheres. Zbl 0817.76043
Liu, M.; Delgado, A.; Rath, H. J.
1994
Decoupling and coefficient assignment for (A,B,C,D) time-delay systems. Zbl 0686.93013
Liu, M. Z.
1989
Convergence rate of the truncated Milstein method of stochastic differential delay equations. Zbl 1429.65026
Zhang, Wei; Yin, Xunbo; Song, M. H.; Liu, M. Z.
2019
Strong convergence of the partially truncated Euler-Maruyama method for a class of stochastic differential delay equations. Zbl 1444.34099
Zhang, Wei; Song, M. H.; Liu, M. Z.
2018
Calabi-Yau properties of nontrivial Noetherian DG down-up algebras. Zbl 1410.16016
Mao, X.-F.; He, J.-W.; Liu, M.; Xie, J.-F.
2018
Convergence and stability of the compensated split-step theta method for stochastic differential equations with piecewise continuous arguments driven by Poisson random measure. Zbl 1391.60166
Lu, Yulan; Song, Minghui; Liu, Mingzhu
2018
Convergence and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Zbl 1376.60066
Lu, Y. L.; Song, M. H.; Liu, M. Z.
2017
Convergence and stability of impulsive stochastic differential equations. Zbl 1391.93285
Song, M. H.; Yang, H. Z.; Liu, M. Z.
2017
Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations. Zbl 1323.34085
Zhang, G. L.; Song, M. H.; Liu, M. Z.
2015
Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments. Zbl 1309.65084
Liu, Xing; Liu, Ming-Zhu
2015
Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations. Zbl 1338.34133
Zhang, G. L.; Song, Minghui; Liu, M. Z.
2015
Stability analysis of Runge-Kutta methods for systems $$u'(t)=Lu(t)+Mu([t])$$. Zbl 1364.65144
Liang, Hui; Liu, M. Z.; Yang, Z. W.
2014
Analytic and numerical exponential asymptotic stability of nonlinear impulsive differential equations. Zbl 1291.65237
Liu, Xing; Zhang, G. L.; Liu, M. Z.
2014
Exponential stability of impulsive delay differential equations. Zbl 1302.34110
Zhang, G. L.; Song, Ming Hui; Liu, Ming Zhu
2013
New iterative method based on Laplace decomposition algorithm. Zbl 1266.65119
Widatalla, Sabir; Liu, M. Z.
2013
Asymptotic stability of a class of impulsive delay differential equations. Zbl 1255.34079
Zhang, G. L.; Song, M. H.; Liu, M. Z.
2012
Linear multistep methods for impulsive differential equations. Zbl 1248.65076
Liu, Xing; Song, M. H.; Liu, M. Z.
2012
Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type. Zbl 1280.65070
Song, Minghui; Liu, Mingzhu
2012
Stability of analytic and numerical solutions for differential equations with piecewise continuous arguments. Zbl 1244.34097
Song, Minghui; Liu, M. Z.
2012
Numerical stability and oscillation of the Runge-Kutta methods for equation $$x'(t)=ax(t)+a_0x(M[\frac{t+N}{M}])$$. Zbl 1416.65210
Song, Minghui; Liu, M. Z.
2012
Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type. Zbl 1207.65103
Wang, Qi; Zhu, Qingyong; Liu, Mingzhu
2011
Stability of the analytic and numerical solutions for impulsive differential equations. Zbl 1233.65044
Liang, Hui; Song, M. H.; Liu, M. Z.
2011
Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics. Zbl 1237.65064
Gao, Jianfang; Song, Minghui; Liu, Mingzhu
2011
Convergence and stability of the semi-implicit Euler method with variable stepsize for a linear stochastic pantograph differential equation. Zbl 1214.65003
Xiao, Yu; Song, Minghui; Liu, Mingzhu
2011
Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients. Zbl 1252.65133
Lv, W. J.; Yang, Z. W.; Liu, M. Z.
2011
Almost surely asymptotic stability of numerical solutions for neutral stochastic delay differential equations. Zbl 1252.65018
Yu, Zhanhua; Liu, Mingzhu
2011
Extinction and permanence of the numerical solution of a two-prey one-predator system with impulsive effect. Zbl 1218.65071
Liang, Hui; Liu, Mingzhu; Song, Minghui
2011
Finite size effects and symmetry breaking in the evolution of networks of competing Boolean nodes. Zbl 1211.37036
Liu, M.; Bassler, K. E.
2011
Stability of the semi-implicit Euler method for a linear impulsive stochastic differential equation. Zbl 1211.65008
Liu, Mingzhu; Zhao, Guihua; Song, Minghui
2011
Stability of $$\theta$$-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments. Zbl 1209.65091
Liang, Hui; Liu, M. Z.; Lv, Wanjin
2010
The Euler scheme and its convergence for impulsive delay differential equations. Zbl 1202.65088
Ding, Xiaohua; Wu, Kaining; Liu, Mingzhu
2010
Exponential stability of Euler-Maruyama solutions for impulsive stochastic differential equations with delay. Zbl 1229.65031
Zhao, Guihua; Song, M. H.; Liu, M. Z.
2010
Numerical simulation of periodic solutions for a class of numerical discretization neural networks. Zbl 1201.34108
Lu, Chun; Ding, Xiaohua; Liu, Mingzhu
2010
The $$\alpha$$th moment stability for the stochastic pantograph equation. Zbl 1206.65021
Fan, Zhencheng; Song, Minghui; Liu, Mingzhu
2009
Preservation of oscillations of the Runge-Kutta method for equation $$x'(t)+ax(t)+a_1x([t - 1])=0$$. Zbl 1189.65143
Liu, M. Z.; Gao, J. F.; Yang, Z. W.
2009
Noise suppresses exponential growth under regime switching. Zbl 1173.60024
Hu, Guangda; Liu, Mingzhu; Mao, Xuerong; Song, Minghui
2009
Noise expresses exponential growth under regime switching. Zbl 1184.93027
Hu, Guangda; Liu, Mingzhu; Mao, Xuerong; Song, Minghui
2009
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations. Zbl 1198.65108
Wang, Qiubao; Li, Dongsong; Liu, M. Z.
2009
Numerical Hopf bifurcation of linear multistep methods for a class of delay differential equations. Zbl 1161.65056
Liu, M. Z.; Wang, Qiubao
2009
Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. Zbl 1180.65094
Yang, Z. W.; Liu, M. Z.; Nieto, Juan J.
2009
Stability and Neimark-Sacker bifurcation in Runge-Kutta methods for a predator-prey system. Zbl 1190.65116
Wang, Qiubao; Liu, M. Z.
2009
Exponential $$p$$-stability of impulsive stochastic differential equations with delays. Zbl 1224.60154
Zhao, Guihua; Liu, Mingzhu; Lü, Wanjin
2009
Periodic solutions for a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay. Zbl 1152.34046
Ding, Xiaohua; Lu, Chun; Liu, Mingzhu
2008
Numerical methods for impulsive differential equation. Zbl 1145.65317
Ran, X. J.; Liu, M. Z.; Zhu, Q. Y.
2008
Mean square stability of stochastic differential equations with piecewise continuous arguments. Zbl 1199.60205
Dai, Hongyu; Liu, Mingzhu
2008
Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback. Zbl 1138.93030
Ding, Xiaohua; Su, Huan; Liu, Mingzhu
2008
Properties of the weighted logarithmic matrix norms. Zbl 1144.15018
Hu, Guang-Da; Liu, Mingzhu
2008
Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations. Zbl 1107.60030
Fan, Zhencheng; Liu, Mingzhu; Cao, Wanrong
2007
Oscillation analysis of numerical solution in the $$\theta$$-methods for equation $$x\prime (t) + ax(t) + a_{1}x([t - 1]) = 0$$. Zbl 1118.65080
Liu, M. Z.; Gao, Jianfang; Yang, Z. W.
2007
Stability of Runge-Kutta methods in the numerical solution of linear impulsive differential equations. Zbl 1193.65121
Liu, M. Z.; Liang, Hui; Yang, Z. W.
2007
Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments. Zbl 1193.65122
Liu, M. Z.; Ma, S. F.; Yang, Z. W.
2007
Stability criteria of linear neutral systems with multiple delays. Zbl 1366.34098
Hu, Guang-Da; Liu, Mingzhu
2007
$$H_{\alpha}$$-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations. Zbl 1125.65076
Ma, S. F.; Yang, Z. W.; Liu, M. Z.
2007
Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments. Zbl 1175.65088
Lv, W. J.; Yang, Z. W.; Liu, M. Z.
2007
Stability and bifurcation of a numerical discretization Mackey-Glass system. Zbl 1132.37030
Ding, Xiaohua; Fan, Dejun; Liu, Mingzhu
2007
Stability of Runge-Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments. Zbl 1140.65057
Lv, W. J.; Yang, Z. W.; Liu, M. Z.
2007
Input-to-state stability of Runge-Kutta methods for nonlinear control systems. Zbl 1114.93090
Hu, Guang-Da; Liu, Mingzhu
2007
The asymptotically mean square stability of the linear stochastic pantograph equation. Zbl 1141.60350
Fan, Zhencheng; Liu, Mingzhu
2007
Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. Zbl 1115.65007
Ding, Xiaohua; Wu, Kaining; Liu, Mingzhu
2006
Stability of a class of Runge–Kutta methods for a family of pantograph equations of neutral type. Zbl 1168.65371
Zhao, J. J.; Xu, Y.; Wang, H. X.; Liu, M. Z.
2006
The stability of modified Runge-Kutta methods for the pantograph equation. Zbl 1094.65075
Liu, M. Z.; Yang, Z. W.; Xu, Y.
2006
Global exponential stability analysis for neutral delay-differential systems: an LMI approach. Zbl 1137.34353
Liu, M.
2006
Stability of $$\theta$$-methods for advanced differential equations with piecewise continuous arguments. Zbl 1082.65078
Song, M. H.; Yang, Z. W.; Liu, M. Z.
2005
Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system. Zbl 1083.65129
Zhao, J. J.; Xu, Y.; Liu, M. Z.
2005
Stability of Runge-Kutta methods in the numerical solution of equation $$u'(t)=au(t)+a_{0} u([t])+a_{1} u([t-1])$$. Zbl 1063.65070
Yang, Zhanwen; Liu, Mingzhu; Song, Minghui
2005
Asymptotical stability of numerical methods with constant stepsize for pantograph equations. Zbl 1095.65075
Liu, M. Z.; Yang, Z. W.; Hu, G. D.
2005
Runge-Kutta methods for the multi-pantograph delay equation. Zbl 1070.65060
Li, D.; Liu, M. Z.
2005
A new modification of Adomian decomposition method for solving a kind of evolution equation. Zbl 1121.65355
Jin, Chengri; Liu, Mingzhu
2005
Stability of the Rosenbrock methods for the neutral delay differential-algebraic equations. Zbl 1081.65079
Zhao, J. J.; Xu, Y.; Dong, S. Y.; Liu, M. Z.
2005
Simple criteria for stability of two-dimensional linear systems. Zbl 1370.93161
Hu, Guang-Da; Liu, Mingzhu
2005
$$P$$-stability of continuous Runge-Kutta-Nyström method for a class of delayed second order differential equation. Zbl 1095.65073
Ding, Xiaohua; Zou, Jinying; Liu, Mingzhu
2005
Analysis and experimental verification of the linear correlation of the operation condition among the bifurcation points of current-mode-controlled buck-boost converter. Zbl 1061.94553
Cheng, K. W. Eric; Liu, M.
2005
Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. Zbl 1059.65006
Liu, Mingzhu; Cao, Wanrong; Fan, Zhencheng
2004
Properties of analytic solution and numerical solution of multi-pantograph equation. Zbl 1059.65060
Liu, M. Z.; Li, Dongsong
2004
MS-stability of the Euler–Maruyama method for stochastic differential delay equations. Zbl 1074.65007
Cao, Wanrong; Liu, Mingzhu; Fan, Zhencheng
2004
Stability of Runge–Kutta methods in the numerical solution of equation $$u'(t)=au(t)+a_{0}u([t])$$. Zbl 1052.65070
Liu, M. Z.; Song, M. H.; Yang, Z. W.
2004
The weighted logarithmic matrix norm and bounds of the matrix exponential. Zbl 1060.15024
Hu, Guang-Da; Liu, Mingzhu
2004
$$\mathcal H$$-stability of Runge-Kutta methods with general variable stepsize for pantograph equation. Zbl 1038.65070
Xu, Yang; Liu, Mingzhu
2004
Asymptotic stability of Runge-Kutta methods for the pantograph equations. Zbl 1065.65102
Zhao, Jingjun; Cao, Wanrong; Liu, Mingzhu
2004
$${\mathcal H}$$-stability of Runge-Kutta methods with variable stepsize for system of pantograph equations. Zbl 1059.65068
Xu, Yang; Zhao, Jingjun; Liu, Mingzhu
2004
Asymptotic stability properties of $$\theta$$-methods for the multi-pantograph delay differential equation. Zbl 1054.65081
Li, Dongsong; Liu, Mingzhu
2004
Hopf bifurcation in numerical approximation of a class delay differential equations. Zbl 1037.34068
Zhang, Chunrui; Liu, Mingzhu; Zheng, Baodong
2003
Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading. Zbl 1038.74613
Liu, M.; Hsia, K. J.
2003
Delay-dependent treatment of linear multistep methods for neutral delay differential equations. Zbl 1059.65062
Jaffer, Syed Khalid; Liu, Mingzhu
2003
Hopf bifurcation in numerical approximation for delay differential equations. Zbl 1042.65055
Zhang, Chunrui; Liu, Mingzhu; Zheng, Baodong
2003
Asymptotic stability for Gauss methods for neutral delay differential equations. Zbl 1002.65087
Sidibe, Birama Sory; Liu, Mingzhu
2002
Delay-dependent stability analysis of Runge-Kutta methods for neutral delay differential equations. Zbl 1067.65083
Sidibe, B. S.; Song, Minghui; Liu, Mingzhu
2002
Convergence aspects of step-parallel iteration of Runge-Kutta methods for delay differential equations. Zbl 1020.65041
Ding, Xiaohua; Liu, Mingzhu
2002
Exact solution properties of a multi-pantograph delay differential equation. Zbl 1087.34536
Li, Dongsong; Liu, Mingzhu
2000
Asymptotic stability of numerical solutions to pantograph delay differential equations. Zbl 0970.65548
Li, Dongsong; Liu, Mingzhu
1999
Estimation of numerically stable step-size for neutral delay-differential equations via spectral radius. Zbl 0868.65054
Hu, Guang-Di; Hu, Guang-Da; Liu, Mingzhu
1997
Stability of numerical solutions to pantograph delay systems. Zbl 0970.65550
Liang, Jiuzhen; Liu, Mingzhu
1996
The stability of $$\theta$$-methods for pantograph delay differential equations. Zbl 0869.65052
Liang, Jiuzhen; Qiu, Shenshan; Liu, Mingzhu
1996
Quantification of mixing in aperiodic chaotic flows. Zbl 0823.76020
Liu, M.; Muzzio, F. J.; Peskin, R. L.
1994
Effects of manifolds and corner singularities on stretching in chaotic cavity flows. Zbl 0816.76026
Liu, M.; Muzzio, F. J.; Peskin, R. L.
1994
A numerical method for study of the unsteady viscous flow between two concentric rotating spheres. Zbl 0817.76043
Liu, M.; Delgado, A.; Rath, H. J.
1994
Three-dimensional infinite boundary elements for contact problems. Zbl 0789.73078
Liu, M.; Farris, T. N.
1993
Criterion for decoupling dynamic equations of motion of linear gyroscopic systems. Zbl 0799.70010
Liu, M.; Wilson, J. M.
1992
The stability of the $$\theta$$-methods in the numerical solution of delay differential equations. Zbl 0693.65056
Liu, M. Z.; Spijker, M. N.
1990
Decoupling and coefficient assignment for (A,B,C,D) time-delay systems. Zbl 0686.93013
Liu, M. Z.
1989
On the solvability of the systems of equations arising in implicit Runge- Kutta methods. Zbl 0661.65078
Liu, M. Z.; Kraaijevanger, J. F. B. M.
1988
Suitability of Runge-Kutta methods. Zbl 0628.65050
Liu, M. Z.; Dekker, K.; Spijker, M. N.
1987
all top 5

#### Cited by 838 Authors

 32 Liu, Mingzhu 24 Huang, Chengming 18 Song, Minghui 17 Zhang, Chengjian 13 Gan, Siqing 13 Liang, Hui 13 Wen, Liping 12 Ding, Xiaohua 12 Sezer, Mehmet 10 Gao, Jianfang 10 Li, Shoufu 10 Wang, Wansheng 10 Yu, Yuexin 9 Hu, Guangda 8 Deng, Feiqi 8 Yang, Zhanwen 8 Zhang, Guilai 7 Mao, Xuerong 7 Tian, Hongjiong 7 Wen, Jiechang 7 Zhou, Shaobo 6 Guo, Qian 6 Wu, Fuke 6 Xiao, Aiguo 6 Xu, Yang 5 Cao, Wanrong 5 Guo, Ping 5 in ’t Hout, Karel J. 5 Liu, Mingzeng 5 Lv, Wanjin 5 Mao, Wei 5 Mitsui, Taketomo 5 Shen, Yi 5 Wang, Jinrong 5 Wang, Qi 5 Wang, Yuanyuan 5 Yu, Zhanhua 5 Yüzbaşı, Şuayip 4 Bhrawy, Ali Hassan 4 Brunner, Hermann 4 Cong, Yuhao 4 Dwivedi, Ravi 4 Fan, Zhencheng 4 Giona, Massimiliano 4 Hu, Liangjian 4 Hu, Peng 4 Hu, Yangzi 4 Li, Chongjun 4 Li, Qiyong 4 Liu, Linna 4 Lu, Hongying 4 Mo, Haoyi 4 Rathinasamy, Anandaraman 4 Sahai, Vivek 4 Wang, Qi 4 Wang, Qiubao 4 Wu, Kaining 4 Yalçinbaş, Salih Fuat 4 Zhang, Chunrui 4 Zhang, Qingling 4 Zhang, Wei 4 Zhao, Jingjun 4 Zheng, Baodong 4 Zhu, Quanxin 3 Adrover, Alessandra 3 Baker, Christopher T. H. 3 Balachandran, Krishnan 3 Băleanu, Dumitru I. 3 Chen, Hao 3 Chiu, Kuo-Shou 3 Cortelezzi, Luca 3 Din, Qamar 3 Ding, Xiaoquan 3 Doha, Eid H. 3 Donchev, Tzanko Donchev 3 Ganji, Davood Domiri 3 Gao, Shujing 3 Gülsu, Mustafa 3 Hu, Junhao 3 Hu, Lin 3 Hu, Shigeng 3 Jiang, Feng 3 Jiang, Xiaowei 3 Kraaijevanger, J. F. B. M. 3 Kuang, Jiaoxun 3 Li, Ronghua 3 Li, Xuguang 3 Li, Yingguo 3 Liu, Maozi 3 Liu, Mingzhuo 3 Liu, Wei 3 Liu, Xing 3 Liu, Xiuxiang 3 Ma, Shufang 3 Muzzio, Fernando J. 3 Nieto Roig, Juan Jose 3 Qiu, Shenshan 3 Schneid, Josef 3 Song, Myung-Ho 3 Teng, Zhi-dong ...and 738 more Authors
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#### Cited in 120 Serials

 110 Applied Mathematics and Computation 50 Journal of Computational and Applied Mathematics 26 International Journal of Computer Mathematics 22 Applied Numerical Mathematics 21 Abstract and Applied Analysis 19 Advances in Difference Equations 18 Journal of the Franklin Institute 16 Discrete Dynamics in Nature and Society 14 Computers & Mathematics with Applications 13 Journal of Applied Mathematics 11 Journal of Mathematical Analysis and Applications 11 Chaos, Solitons and Fractals 11 Applied Mathematics Letters 9 BIT 8 Mathematical Methods in the Applied Sciences 8 Journal of Difference Equations and Applications 8 Frontiers of Mathematics in China 7 Applied Mathematical Modelling 7 Mathematical Problems in Engineering 7 Journal of Applied Mathematics and Computing 6 Numerische Mathematik 6 Mathematical and Computer Modelling 6 Communications in Nonlinear Science and Numerical Simulation 5 Numerical Methods for Partial Differential Equations 5 Physics of Fluids 5 Computational and Applied Mathematics 5 Journal of Inequalities and Applications 5 Nonlinear Analysis. Hybrid Systems 4 Linear and Multilinear Algebra 4 Automatica 4 Numerical Functional Analysis and Optimization 4 Acta Applicandae Mathematicae 4 Journal of Scientific Computing 4 Nonlinear Dynamics 4 Journal of Systems Science and Complexity 3 International Journal of Systems Science 3 Journal of Fluid Mechanics 3 Mathematics of Computation 3 Kybernetika 3 Mathematics and Computers in Simulation 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Acta Mathematicae Applicatae Sinica. English Series 3 Numerical Algorithms 3 Applied Mathematics. Series B (English Edition) 3 Advances in Computational Mathematics 3 Engineering Analysis with Boundary Elements 3 Nonlinear Analysis. Real World Applications 3 International Journal of Fracture 2 Acta Mechanica 2 Communications in Algebra 2 International Journal of Control 2 Journal of Computational Physics 2 Physica A 2 Calcolo 2 Physica D 2 Journal of Mathematical Chemistry 2 Chaos 2 Discrete and Continuous Dynamical Systems. Series B 2 International Journal of Biomathematics 2 Advances in Mathematical Physics 2 International Journal of Differential Equations 2 Journal of Mathematics 2 Journal of Function Spaces 2 Asia Pacific Journal of Mathematics 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Computers and Fluids 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Lithuanian Mathematical Journal 1 Rocky Mountain Journal of Mathematics 1 Glasgow Mathematical Journal 1 International Journal of Circuit Theory and Applications 1 International Journal for Numerical Methods in Engineering 1 Journal of Algebra 1 Mathematische Nachrichten 1 Meccanica 1 Siberian Mathematical Journal 1 Statistics & Probability Letters 1 Applied Mathematics and Mechanics. (English Edition) 1 Science in China. Series A 1 Multidimensional Systems and Signal Processing 1 Applications of Mathematics 1 SIAM Review 1 Acta Mechanica Sinica. (English Edition) 1 Journal of Dynamics and Differential Equations 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 SIAM Journal on Scientific Computing 1 Communications in Numerical Methods in Engineering 1 Numerical Linear Algebra with Applications 1 Integral Transforms and Special Functions 1 European Journal of Control 1 Doklady Mathematics 1 Vietnam Journal of Mathematics 1 Journal of Applied Mathematics and Decision Sciences 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Acta Mathematica Sinica. English Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Stochastics and Dynamics 1 SIAM Journal on Applied Dynamical Systems ...and 20 more Serials
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#### Cited in 34 Fields

 361 Numerical analysis (65-XX) 312 Ordinary differential equations (34-XX) 140 Probability theory and stochastic processes (60-XX) 71 Systems theory; control (93-XX) 58 Biology and other natural sciences (92-XX) 44 Integral equations (45-XX) 32 Partial differential equations (35-XX) 29 Dynamical systems and ergodic theory (37-XX) 19 Difference and functional equations (39-XX) 18 Fluid mechanics (76-XX) 14 Mechanics of deformable solids (74-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 10 Special functions (33-XX) 8 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Associative rings and algebras (16-XX) 4 Mechanics of particles and systems (70-XX) 4 Operations research, mathematical programming (90-XX) 3 Combinatorics (05-XX) 3 Approximations and expansions (41-XX) 3 Computer science (68-XX) 3 Information and communication theory, circuits (94-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX)