Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity

Journal Article · Wed Feb 15 00:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.73.044001· OSTI ID:20776739

Leiler, Gregor ^[1]; Rezzolla, Luciano ^[2]

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1. Department of Physics, Udine University, Udine (Italy)
2. Max-Planck-Institut fuer Gravitationsphysik, Albert Einstein Institut, Golm (Germany)

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.

• OSTI ID: 20776739
• Journal Information: Physical Review. D, Particles Fields, Vol. 73, Issue 4; Other Information: DOI: 10.1103/PhysRevD.73.044001; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
AMPLIFICATION
CORRECTIONS
COSMOLOGY
GENERAL RELATIVITY THEORY
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
STABILITY