Stability of the iterated Crank-Nicholson method in numerical relativity

Saul A. Teukolsky
Phys. Rev. D 61, 087501 – Published 14 March 2000
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Abstract

The iterated Crank-Nicholson method has become a popular algorithm in numerical relativity. We show that one should carry out exactly two iterations and no more. While the limit of an infinite number of iterations is the standard Crank-Nicholson method, it can in fact be worse to do more than two iterations, and it never helps. We explain how this paradoxical result arises.

  • Received 7 September 1999

DOI:https://doi.org/10.1103/PhysRevD.61.087501

©2000 American Physical Society

Authors & Affiliations

Saul A. Teukolsky

  • Newman Laboratory, Cornell University, Ithaca, New York 14853

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Vol. 61, Iss. 8 — 15 April 2000

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