Relaxation Exponential Runge-Kutta Methods and Their Applications to Semilinear Dissipative/Conservative Systems
Year: 2024
Author: Dongfang Li, Xiaoxi Li, Jiang Yang
Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 908–942
Abstract
This paper presents a family of novel relaxation exponential Runge-Kutta methods for semilinear partial differential equations with dissipative/conservative energy. The novel methods are developed by using the relaxation idea and adding a well-designed governing equation to explicit exponential Runge-Kutta methods. It is shown that the proposed methods can be of high-order accuracy and energy-stable/conserving with mild time step restrictions. In contrast, the previous explicit exponential-type methods are not energy-conserving. Several numerical experiments on KdV equations, Schrödinger equations and Navier-Stokes equations are carried out to illustrate the effectiveness and high efficiency of the methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0241
Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 908–942
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Explicit exponential Runge-Kutta methods relaxation technique high-order accuracy structure-preserving property.
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