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Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential Equations

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  • Wei Gu
  • Ming Wang
  • Dongfang Li

Abstract

The present paper is concerned with the relationship between stepsize restriction and nonlinear stability of Runge‐Kutta methods for delay differential equations. We obtain a special stepsize condition guaranteeing global and asymptotical stability properties of numerical methods. Some confirmations of the conditions on Runge‐Kutta methods are illustrated at last.

Suggested Citation

  • Wei Gu & Ming Wang & Dongfang Li, 2014. "Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:304071
    DOI: 10.1155/2014/304071
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    References listed on IDEAS

    as
    1. Dongfang Li & Chao Tong & Jinming Wen, 2014. "Stability of Exact and Discrete Energy for Non‐Fickian Reaction‐Diffusion Equations with a Variable Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    3. Ali H. Bhrawy & Abdulrahim AlZahrani & Dumitru Baleanu & Yahia Alhamed, 2014. "A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
    4. E. H. Doha & D. Baleanu & A. H. Bhrawy & R. M. Hafez, 2014. "A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi‐Infinite Interval Using Legendre Rational Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. E. H. Doha & D. Baleanu & A. H. Bhrawy & R. M. Hafez, 2014. "A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, May.
    6. Dongfang Li & Chao Tong & Jinming Wen, 2014. "Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
    7. Ali H. Bhrawy & Abdulrahim AlZahrani & Dumitru Baleanu & Yahia Alhamed, 2014. "A Modified Generalized Laguerre‐Gauss Collocation Method for Fractional Neutral Functional‐Differential Equations on the Half‐Line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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