SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Automated design and analysis of ODE solvers

D. Ketcheson and M. Parsani

Abstract
Decades of research have led to a wealth of detailed knowledge about properties of numerical ODE solvers - their accuracy, stability, efficiency, structure preservation, and so forth. The process of applying this knowledge to the study of existing methods and the design of new ones can be fully automated. I will describe ongoing efforts to create a software laboratory whose ultimate goal is to tell you everything you might want to know about a given method, help you select an appropriate method for a given problem, or even design a new method that is particularly effective for a given problem. Some examples will be given to demonstrate the power of these tools in the context of applications like compressible fluid flow.

Bibliography
[1] D.I. Ketcheson, NodePy software version 0.4, http://numerics.kaust.edu.sa/nodepy/
[2] D.I. Ketcheson, M. Parsani and A. Ahmadia, RK-Opt software version 0.4, http://numerics.kaust.edu.sa/RK-Opt/
[3] D.I. Ketcheson, Umair bin Waheed, A theoretical comparison of high order explicit Runge-Kutta, extrapolation, and deferred correction methods, http://arxiv.org/abs/1305.6165, submitted.
[4] M. Parsani, D.I. Ketcheson, and W. Deconinck, Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems, SIAM J. Sci. Comput. 35(2): A957-A986.

Organized by         Universidad de Valladolid     IMUVA