TY - JOUR
T1 - Relaxation Exponential Runge-Kutta Methods and Their Applications to Semilinear Dissipative/Conservative Systems
AU - Li , Dongfang
AU - Li , Xiaoxi
AU - Yang , Jiang
JO - Communications in Computational Physics
VL - 4
SP - 908
EP - 942
PY - 2024
DA - 2024/10
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0241
UR - https://global-sci.org/intro/article_detail/cicp/23481.html
KW - Explicit exponential Runge-Kutta methods, relaxation technique, high-order accuracy, structure-preserving property.
AB - <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>