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Asymptotical Stability of Numerical Methods with Constant Stepsize for Pantograph Equations

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Abstract

In this paper, the asymptotical stability of the analytic solution and the numerical methods with constant stepsize for pantograph equations is investigated using the Razumikhin technique. In particular, the linear pantograph equations with constant coefficients and variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the θ-methods with constant stepsize are obtained. As a result Z. Jackiewicz’s conjecture is partially proved. Finally, some experiments are given.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    M. Z. Liu & Z. W. Yang

  2. Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

    G. D. Hu

Authors
  1. M. Z. Liu
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  2. Z. W. Yang
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  3. G. D. Hu
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Correspondence to M. Z. Liu.

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AMS subject classification (2000)

65L02, 65L05, 65L20

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Liu, M., Yang, Z. & Hu, G. Asymptotical Stability of Numerical Methods with Constant Stepsize for Pantograph Equations. Bit Numer Math 45, 743–759 (2005). https://doi.org/10.1007/s10543-005-0022-3

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  • DOI: https://doi.org/10.1007/s10543-005-0022-3

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