Abstract
Exponential integrators are becoming increasingly popular for stiff problems of high dimension due to their attractive property of solving the linear part of the system exactly and hence being A-stable. In practice, however, exponential integrators are implemented using approximation techniques to matrix-vector products involving functions of the matrix exponential (the so-called \(\varphi \)-functions) to make them efficient and competitive to other state-of-the-art schemes. We will examine linear stability and provide a Courant–Friedrichs–Lewy (CFL) condition of special classes of exponential integrator schemes called EPIRK and sEPIRK and demonstrate their dependence on the parameters of the embedded approximation technique. Furthermore, a conservation property of the EPIRK schemes is proven.
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Acknowledgements
We thank the German Research Foundation DFG for its financial support within the project GZ: ME 1889/7-1.
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Birken, P., Meister, A., Ortleb, S., Straub, V. (2018). On Stability and Conservation Properties of (s)EPIRK Integrators in the Context of Discretized PDEs. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_46
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DOI: https://doi.org/10.1007/978-3-319-91548-7_46
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