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Journal of Scientific Computing

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01.09.2016

Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability

verfasst von: Michał Braś, Giuseppe Izzo, Zdzisław Jackiewicz

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2017

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Abstract

We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is \(A(\alpha )\)-stable for some \(\alpha \in (0,\pi /2]\). Examples of highly stable IMEX GLMs are provided of order \(1\le p\le 4\). Numerical examples are also given which illustrate good performance of these schemes.

Vorheriger Artikel Nonlinear Advection–Diffusion–Reaction Phenomena Involved in the Evolution and Pumping of Oil in Open Sea: Modeling, Numerical Simulation and Validation Considering the Prestige and Oleg Naydenov Oil Spill Cases

Nächster Artikel Two-Level Penalty Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics Equations

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Titel: Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability
verfasst von: Michał Braś
Giuseppe Izzo
Zdzisław Jackiewicz
Publikationsdatum: 01.09.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0273-y

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