On the iterated Crank-Nicolson for hyperbolic and parabolic equations in numerical relativity

Details On the iterated Crank-Nicolson for hyperbolic and parabolic equations in numerical relativity On the iterated Crank-Nicolson for hyperbolic and parabolic equations in numerical relativity

2006-01-31

arxiv.org/abs/gr-qc/0601139v1

Phys.Rev. D73 (2006) 044001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, 3 figures

Scientific paper

10.1103/PhysRevD.73.044001

The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic equations by investigating the properties when the average between the predicted and corrected values is made with unequal weights and when the scheme is applied to a parabolic equation. We also propose a variant of the scheme in which the coefficients in the averages are swapped between two corrections leading to systematically larger amplification factors and to a smaller numerical dispersion.

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