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Volume 9, Issue 3
A Fast Compact Exponential Time Differencing Runge-Kutta Method for Time-Dependent Advection-Diffusion-Reaction Equations

Xueyun Xie & Liyong Zhu

DOI: 10.4208/eajam.170618.101018

East Asian J. Appl. Math., 9 (2019), pp. 522-537.

Published online: 2019-06

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  • Abstract

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.

  • Keywords

Advection-diffusion-reaction, exponential time differencing, linear splitting, discrete Fourier transforms, Runge-Kutta approximations.

  • AMS Subject Headings

65M06, 65M22, 65Y20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-522, author = {Xueyun Xie and Liyong Zhu}, title = {A Fast Compact Exponential Time Differencing Runge-Kutta Method for Time-Dependent Advection-Diffusion-Reaction Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {3}, pages = {522--537}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.170618.101018 }, url = {http://global-sci.org/intro/article_detail/eajam/13165.html} }
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 -

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.

Xueyun Xie and Liyong Zhu. (2019). A Fast Compact Exponential Time Differencing Runge-Kutta Method for Time-Dependent Advection-Diffusion-Reaction Equations. East Asian Journal on Applied Mathematics. 9 (3). 522-537. doi:10.4208/eajam.170618.101018
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