TY - JOUR
T1 - A Fast Compact Exponential Time Differencing Runge-Kutta Method for Time-Dependent Advection-Diffusion-Reaction Equations
AU - Xueyun Xie & Liyong Zhu
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 522
EP - 537
PY - 2019
DA - 2019/06
SN - 9
DO - http://doi.org/10.4208/eajam.170618.101018 
UR - https://global-sci.org/intro/article_detail/eajam/13165.html
KW - Advection-diffusion-reaction, exponential time differencing, linear splitting, discrete
Fourier transforms, Runge-Kutta approximations.
AB - <p style="text-align: justify;">A fast and accurate exponential Runge-Kutta method for a class of time-dependent advection-diffusion-reaction equations is developed. To discretise the convection term, a modified upwind difference scheme is used. This allows to avoid numerical
oscillation and achieve second order spatial accuracy. The method demonstrates good
stability and numerical examples show the applicability of the method to advection-diffusion-reaction problems with stiff nonlinearities.</p>