@Article{CiCP-36-908,
author = {Li , DongfangLi , Xiaoxi and Yang , Jiang},
title = {Relaxation Exponential Runge-Kutta Methods and Their Applications to Semilinear Dissipative/Conservative Systems},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {4},
pages = {908--942},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0241},
url = {http://global-sci.org/intro/article_detail/cicp/23481.html}
}