A Fast Compact Exponential Time Differencing Runge-Kutta Method for Time-Dependent Advection-Diffusion-Reaction Equations
Year: 2019
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.170618.101018
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 3 : pp. 522–537
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Advection-diffusion-reaction exponential time differencing linear splitting discrete Fourier transforms Runge-Kutta approximations.