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Izzo, Giuseppe; Jackiewicz, Zdzislaw

Strong stability preserving implicit-explicit transformed general linear methods. (English) Zbl 1510.65144

Math. Comput. Simul. 176, 206-225 (2020).
Summary: We consider the class of implicit-explicit (IMEX) general linear methods (GLMs) to construct methods where the explicit part has strong stability preserving (SSP) property, while the implicit part of the method has inherent Runge-Kutta stability (IRKS) property, and it is \(A\)-, or \(L\)-stable. We will also investigate the absolute stability of these methods when the implicit and explicit parts interact with each other. In particular, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is \(A ( \alpha )\)-stable for \(\alpha \in [0, \pi/2]\). Finally we furnish examples of SSP IMEX GLMs up to the order \(p = 4\) and stage order \(q = p\) with optimal SSP coefficients.

Cited in 4 Documents

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations

Keywords:

IMEX methods; SSP property; general linear methods; stability analysis; inherent Runge-Kutta stability; construction of highly stable methods

Software:

RODAS; ODEPACK
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Full Text: DOI

References:

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