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Relaxation Exponential Runge-Kutta Methods and Their Applications to Semilinear Dissipative/Conservative Systems

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.

Author Details

Dongfang Li

Xiaoxi Li

Jiang Yang

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