Abstract
Exponential Runge–Kutta methods are tailored for the time discretization of semilinear stiff problems. The actual construction of high-order methods relies on the knowledge of the order conditions, which are available in the literature up to order four. In this short note, we show how the order conditions for methods up to order five are derived; the extension to arbitrary orders will be published elsewhere. Our approach is adapted to stiff problems and allows us to prove high-order convergence results for variable step size implementations, independently of the stiffness of the problem.
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Acknowledgements
This work was supported by the FWF doctoral program ‘Computational Interdisciplinary Modelling’ W1227. The work of the first author was partially supported by the Tiroler Wissenschaftsfond grant UNI-0404/1284.
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Luan, V.T., Ostermann, A. (2014). Stiff Order Conditions for Exponential Runge–Kutta Methods of Order Five. In: Bock, H., Hoang, X., Rannacher, R., Schlöder, J. (eds) Modeling, Simulation and Optimization of Complex Processes - HPSC 2012. Springer, Cham. https://doi.org/10.1007/978-3-319-09063-4_11
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DOI: https://doi.org/10.1007/978-3-319-09063-4_11
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