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Linear Multistep Methods for Impulsive Differential Equations

Author

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  • X. Liu
  • M. H. Song
  • M. Z. Liu

Abstract

This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and two-step BDF method are of order p = 0 when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.

Suggested Citation

  • X. Liu & M. H. Song & M. Z. Liu, 2012. "Linear Multistep Methods for Impulsive Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-14, May.
    • Handle: RePEc:hin:jnddns:652928
    DOI: 10.1155/2012/652928
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    Cited by:

    1. Liu, X. & Zeng, Y.M., 2019. "Analytic and numerical stability of delay differential equations with variable impulses," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 293-304.
    2. Hartung, Ferenc, 2022. "On numerical approximation of a delay differential equation with impulsive self-support condition," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    3. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    4. Zhang, Gui-Lai, 2022. "Convergence, consistency and zero stability of impulsive one-step numerical methods," Applied Mathematics and Computation, Elsevier, vol. 423(C).

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