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References

  • 1
    S. M. Shah and J. Wiener, Advanced differential equations with piecewise constant argument deviations, Int J Math Math Sci 6 (1983), 671703.
  • 2
    J. Wiener, Differential equations with piecewise constant delays, V. Lakshmikantham, editor, Trends in the theory and practice of nonlinear differential equations, Marcel Dekker, New York, (1983).
  • 3
    J. Wiener, Pointwise, initial-value problems for functional differential equations, I. W. Knowles and R. T. Lewis, editors, Differential equations, North-Holland, New York, 1984.
  • 4
    Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J Math Anal Appl 270 (2002), 602-635.
  • 5
    M. U. Akhmet, D. Arugâslanc, and E. Y1lmaz, Stability in cellular neural networks with a piecewise constant argument, J Comput Appl Math 233 (2010), 23652373.
  • 6
    M. U. Akhmet, D. Arugâslanc, and E. Y1lmaz, Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Netw 23 (2010), 805811.
  • 7
    S. Busenberg and K. L. Cooke, Models of vertically transmitted diseases with sequential-continuous dynamics, V. Lakshmikantham, editor, Nonlinear phenomena in mathematical sciences, Academic Press, New York, 1982, pp. 179-187.
  • 8
    K. L. Cooke and J. Wiener, Retarded differential equations with piecewise constant delays, J Math Anal Appl 99 (1984), 265297.
  • 9
    J. Wiener, Generalized solutions of functional differential equations, World Scientific, Singapore, 1993.
  • 10
    L. Dai and M. C. Singh, On oscillatory motion of spring-mass systems subjected to piecewise constant forces, J Sound Vib 173 (1994), 217232.
  • 11
    N. M. Murad and A. Celeste, Linear and nonlinear characterization of loading systems under piecewise discontinuous disturbances voltage: Analytical and numerical approaches Proceedings of International Conference on Power Electronics Systems and Applications Power Electronics Research Centre, The Hong Kong Polytechnic University Hong Kong, China November 2004, pp. 291297.
  • 12
    J. Wiener and V. Lakshmikantham, A damped oscillator with piecewise constant time delay, Nonlinear Stud 1 (2000), 7884.
  • 13
    H. X. Li, Y. Muroya, Y. Nakata, and R. Yuan, Global stability of nonautonomous logistic equations with a piecewise constant delay, Nonlinear Anal Real 11 (2010), 21152126.
  • 14
    X. L. Fu and X. D. Li, Oscillation of higher order impulsive differential equations of mixed type with constant argument at fixed time, Math Comput Model 48 (2008), 776786.
  • 15
    G. Q. Wang, Periodic solutions of a neutral differential equation with piecewise constant arguments, J Math Anal Appl 326 (2007), 736747.
  • 16
    C. Y. Zhang and L. N. Jiang, Remotely almost periodic solutions to systems of differential equations with piecewise constant argument, Appl Math Lett 21 (2008), 761768.
  • 17
    E. Ait Dads and L. Lhachimi, Pseudo almost periodic solutions for equation with piecewise constant argument, J Math Anal Appl 371 (2010), 842854.
  • 18
    Y. Muroya, New contractivity condition in a population model with piecewise constant arguments, J Math Anal Appl 346 (2008), 6581.
  • 19
    M. U. Akhmet and E. Y1lmaz, Impulsive Hopfield-type neural network system with piecewise constant argument, Nonlinear Anal Real 11 (2010), 25842593.
  • 20
    W. Dimbour, Almost automorphic solutions for differential equations with piecewise constant argument in a Banach space, Nonlinear Anal 74 (2011), 23512357.
  • 21
    H. H. Liang and G. Q. Wang, Oscillation criteria of certain third-order differential equation with piecewise constant argument, J Appl Math 2012 (2012), 118.
  • 22
    M. Z. Liu, M. H. Song, and Z. W. Yang, Stability of Runge-Kutta methods in the numerical solution of equation inline image, J Comput Appl Math 166 (2004), 361370.
  • 23
    M. H. Song, Z. W. Yang, and M. Z. Liu, Stability of θ-methods for advanced differential equations with piecewise continuous arguments, Comput Math Appl 49 (2005), 12951301.
  • 24
    Z. W. Yang, M. Z. Liu, and M. H. Song, Stability of Runge-Kutta methods in the numerical solution of equation inline image, Appl Math Comput 162 (2005), 3750.
  • 25
    W. J. Lv, Z. W. Yang, and M. Z. Liu, Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments, Appl Math Comput 186 (2007), 14801487.
  • 26
    M. H. Song and X. Liu, The improved linear multistep methods for differential equations with piecewise continuous arguments, Appl Math Comput 217 (2010), 40024009.
  • 27
    W. J. Lv, Z. W. Yang, and M. Z. Liu, Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients, Appl Math Comput 218 (2011), 4554.
  • 28
    M. Z. Liu, J. F. Gao, and Z. W. Yang, Oscillation analysis of numerical solution in the θ-methods for equation inline image. Appl Math Comput 186 (2007), 566578.
  • 29
    M. Z. Liu, J. F. Gao, and Z. W. Yang, Preservation of oscillations of the Runge-Kutta method for equation inline image. Comput Math Appl 58 (2009), 11131125.
  • 30
    W. S. Wang and S. F. Li, Dissipativity of Runge-Kutta methods for neutral delay differential equations with piecewise constant delay, Appl Math Lett 21 (2008), 983991.
  • 31
    M. H. Song and M. Z. Liu, Stability of analytic and numerical solutions for differential equations with piecewise continuous arguments, Abstr Appl Anal 2012 (2012), 114.
  • 32
    M. Z. Liu, S. F. Ma, and Z. W. Yang, Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments, Appl Math Comput 191 (2007), 5766.
  • 33
    Q. Wang, Q. Y. Zhu, and M. Z. Liu, Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type, J Comput Appl Math 235 (2011), 15421552.
  • 34
    Q. Wang and Q. Y. Zhu, Stability analysis of Runge-Kutta methods for differential equations with piecewise continuous arguments of mixed type, Int J Comput Math 88 (2011), 10521066.
  • 35
    H. Liang, M. Z. Liu and W. J. Lv, Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments, Appl Math Lett 23 (2010), 198206.
  • 36
    H. Liang, D. Y. Shi, and W. J. Lv, Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument, Appl Math Comput 217 (2010), 854860.
  • 37
    J. Wiener, Boundary value problems for partial differential equations with piecewise constant delay, Int J Math Math Sci 14 (1991), 301321.
  • 38
    J. Wiener and L. Debnath, A wave equation with discontinuous time delay, Int J Math Math Sci 15 (1992), 781788.
  • 39
    C. W. Xu, Introduction to computing method, Higher Education Press, Beijing, 1985.