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Uri Ascher, Steven Ruuth and Raymond Spiteri (1997)

Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

Applied Numerical Mathematics, 25(2):151-167.

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 (Ascher et al., 1995). 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.

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