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Explicit exponential Runge–Kutta methods for semilinear parabolic delay differential equations

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  • Zhao, Jingjun
  • Zhan, Rui
  • Xu, Yang

Abstract

This paper is concerned with explicit exponential Runge–Kutta methods for semilinear parabolic delay differential equations. Stiff convergence and conditional DN-stability of explicit exponential Runge–Kutta methods are investigated in the framework of analytic semigroup on a Banach space. We derive the stiff convergence order conditions up to order four. In particular, it is shown that explicit exponential Runge–Kutta methods are conditionally DN-stable. Finally, numerical experiments are presented to validate the convergence results.

Suggested Citation

  • Zhao, Jingjun & Zhan, Rui & Xu, Yang, 2020. "Explicit exponential Runge–Kutta methods for semilinear parabolic delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 366-381.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:366-381
    DOI: 10.1016/j.matcom.2020.06.025
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    References listed on IDEAS

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    1. Zhao, Jingjun & Zhan, Rui & Xu, Yang, 2018. "D-convergence and conditional GDN-stability of exponential Runge–Kutta methods for semilinear delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 45-58.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
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