Discrete boundary treatment for the shifted wave equation

Details Discrete boundary treatment for the shifted wave equation Discrete boundary treatment for the shifted wave equation

2005-09-29

arxiv.org/abs/gr-qc/0509119v2

Class.Quant.Grav. 23 (2006) S343-S368

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 2 figures. Revised version

Scientific paper

We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and time-like boundaries, with either second or fourth order accuracy. These discrete boundary conditions suggest a general prescription for boundary conditions in finite difference codes approximating first order in time, second order in space hyperbolic problems, such as those that appear in numerical relativity. As an example we construct boundary conditions for the Nagy-Ortiz-Reula formulation of the Einstein equations coupled to a scalar field in spherical symmetry.

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