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Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments

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  • Minghui Song
  • M. Z. Liu

Abstract

In this paper, the asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov methods. In particular, the linear equations with variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the θ‐methods are obtained. Some examples are illustrated.

Suggested Citation

  • Minghui Song & M. Z. Liu, 2012. "Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:258329
    DOI: 10.1155/2012/258329
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    References listed on IDEAS

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    1. S. M. Shah & Joseph Wiener, 1983. "Advanced differential equations with piecewise constant argument deviations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-33, January.
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    Cited by:

    1. Qi Wang & Jiechang Wen & Shenshan Qiu, 2013. "Euler‐Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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