Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-12-19
J. Comput. Phys. (2010)
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
36 pages, 10 figures
Scientific paper
10.1016/j.jcp.2009.12.016
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order derivatives that can be identified with advection terms are approximated with non-centered finite difference operators.We first derive general properties of these discrete operators, then we extend a known result on numerical stability for such systems to general order of accuracy.As an application we analyze the shifted wave equation, including the behavior of the numerical phase and group speeds at different orders of approximations. Special attention is paid to when the use of off-centered schemes improves the accuracy over the centered schemes.
Chirvasa Mihaela
Husa Sascha
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