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Linear multistep methods for impulsive delay differential equations

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  • Liu, X.
  • Zeng, Y.M.

Abstract

This paper deals with the convergence and stability of linear multistep methods for a class of linear impulsive delay differential equations. Numerical experiments show that the Simpson’s Rule and two-step BDF method are of order p=0 when applied to impulsive delay differential equations. An improved linear multistep numerical process is proposed. Convergence and stability conditions of the numerical solutions are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.

Suggested Citation

  • Liu, X. & Zeng, Y.M., 2018. "Linear multistep methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 555-563.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:555-563
    DOI: 10.1016/j.amc.2017.11.014
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    References listed on IDEAS

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    1. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
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    Cited by:

    1. 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.
    2. Zuo, Hujian & Zhao, Weifeng & Lin, Ping, 2022. "Boundary treatment of linear multistep methods for hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. 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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