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Faster SDC convergence on non-equidistant grids by DIRK sweeps

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Abstract

Spectral deferred correction methods for solving stiff ODEs are known to converge reasonably fast towards the collocation limit solution on equidistant grids, but show a less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples.

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Acknowledgments

The author is indebted to Bodo Erdmann for many fruitful discussions and thorough computational assistance. Partial funding by the DFG Research Center Matheon “Mathematics for key technologies”, projects A17 and F9, is gratefully acknowledged.

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  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Martin Weiser

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  1. Martin Weiser
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Correspondence to Martin Weiser.

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Communicated by Mechthild Thalhammer.

Supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin, Projects A17 and F9. A preprint is available as ZIB Report 13-30.

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Weiser, M. Faster SDC convergence on non-equidistant grids by DIRK sweeps. Bit Numer Math 55, 1219–1241 (2015). https://doi.org/10.1007/s10543-014-0540-y

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