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Stability of Exact and Discrete Energy for Non‐Fickian Reaction‐Diffusion Equations with a Variable Delay

Author

Listed:
  • Dongfang Li
  • Chao Tong
  • Jinming Wen

Abstract

This paper is concerned with the stability of non‐Fickian reaction‐diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. Then, we prove that the proposed numerical methods are sufficient to preserve energy stability of the continuous problems. We end the paper with some numerical experiments on a biological model to confirm the theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:840573
    DOI: 10.1155/2014/840573
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    References listed on IDEAS

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    1. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    2. Ravi P. Agarwal & Leonid Berezansky & Elena Braverman & Alexander Domoshnitsky, 2012. "Nonoscillation Theory of Functional Differential Equations with Applications," Springer Books, Springer, edition 127, number 978-1-4614-3455-9, March.
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    Cited by:

    1. 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).

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