A Two-Step RKC Method for Time-Dependent PDEs
- CWI, P.O. Box 94079, 1090 GB Amsterdam (Netherlands)
An integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and stiff reaction terms implicitly. The method is a special two-step form of the one-step IMEX (IMplicit-EXplicit) RKC (Runge-Kutta-Chebyshev) method. The special two-step form is introduced with the aim of getting a non-zero imaginary stability boundary which is zero for the one-step method. Having a non-zero imaginary stability boundary allows, for example, the integration of pure advection equations space-discretized with centered schemes, the integration of damped or viscous wave equations, the integration of coupled sound and heat flow equations, etc. For our class of methods it also simplifies the choice of temporal step sizes satisfying the von Neumann stability criterion, by embedding a thin long rectangle inside the stability region.
- OSTI ID:
- 21251357
- Journal Information:
- AIP Conference Proceedings, Vol. 1048, Issue 1; Conference: International conference on numerical analysis and applied mathematics 2008, Psalidi, Kos (Greece), 16-20 Sep 2008; Other Information: DOI: 10.1063/1.2991077; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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