Invited Lecture
Strong stability preserving implicit-explicit transformed general linear methods
Arizona State University, AZ, USA, and AGH University of Science and Technology, Poland
Abstract
For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) general linear methods (GLMs), where the stiff part is integrated by implicit formula, and the non-stiff part is integrated by an explicit formula. We will construct methods where the explicit part has strong stability preserving (SSP) property, and the implicit part of the method has inherent Runge-Kutta stability (IRKS) property, and it is $A$-, or $L$-stable. We will also investigate stability of these methods when the implicit and explicit parts interact with each other. To be more precise, 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.
This is joint work with Giuseppe Izzo, Università degli Studi di Napoli Federico II, Italy
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