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  Numerical stability for finite difference approximations of Einstein's equations

Calabrese, G., Hinder, I., & Husa, S. (2006). Numerical stability for finite difference approximations of Einstein's equations. Journal of Computational Physics, 218, 607-634.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4B10-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4B12-B
Genre: Journal Article

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 Creators:
Calabrese, Gioel, Author
Hinder, Ian1, Author              
Husa, Sascha1, Author              
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1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24013              

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 Abstract: We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in numerical relativity and, more generally, in Hamiltonian formulations of field theories. By analyzing the symbol of the second order system, we obtain necessary and sufficient conditions for stability in a discrete norm containing one-sided difference operators. We prove stability for certain toy models and the linearized Nagy–Ortiz–Reula formulation of Einstein’s equations. We also find that, unlike in the fully first order case, standard discretizations of some well-posed problems lead to unstable schemes and that the Courant limits are not always simply related to the characteristic speeds of the continuum problem. Finally, we propose methods for testing stability for second order in space hyperbolic systems.

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Language(s): eng - English
 Dates: 2006
 Publication Status: Published in print
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 Identifiers: eDoc: 214027
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Title: Journal of Computational Physics
Source Genre: Journal
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Pages: - Volume / Issue: 218 Sequence Number: - Start / End Page: 607 - 634 Identifier: -