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

Jingjun Zhao, Rui Zhan and Yang Xu

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 178, issue C, 366-381

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.

Keywords: Semilinear parabolic delay differential equation; Explicit exponential Runge–Kutta method; Stiff convergence; Conditional DN-stability (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:178:y:2020:i:c:p:366-381

DOI: 10.1016/j.matcom.2020.06.025

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