Implicit-Explicit Runge-Kutta Methods for Time-Dependent Partial Differential Equations (1997)
| Venue: | Appl. Numer. Math |
| Citations: | 66 - 3 self |
BibTeX
@ARTICLE{Ascher97implicit-explicitrunge-kutta,
author = {Uri M. Ascher and Steven J. Ruuth and Raymond J. Spiteri},
title = {Implicit-Explicit Runge-Kutta Methods for Time-Dependent Partial Differential Equations},
journal = {Appl. Numer. Math},
year = {1997},
volume = {25},
pages = {151--167}
}
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Abstract
Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved useful in many applications. However, they tend to have undesirable time-step restrictions when applied to convection-diffusion problems, unless diffusion strongly dominates and an appropriate BDF-based scheme is selected [2]. In this paper, we develop Runge-Kutta-based IMEX schemes that have better stability regions than the best known IMEX multistep schemes over a wide parameter range. 1 Introduction When a time-dependent partial differential equation (PDE) involves terms of different types, it is a natural idea to employ different discretizations for them. Implicit-explicit (IMEX) time-discretization schemes are an example of such a strategy. Linear multistep IMEX schemes have been used by many researchers, especially in conjunction with spectral methods [10, 3]. Some schemes of this type were proposed and analyzed as far back as the late 1970's [15, 5]. Instances of...
