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Numerical integration of the axisymmetric Robinson-Trautman equation by a spectral method

Published online by Cambridge University Press:  17 February 2009

D. A. Prager  and
A. W.-C. Lun
D. A. Prager
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
A. W.-C. Lun
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
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Abstract

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We have adapted the Spectral Transform Method, a technique commonly used in non-linear meteorological problems, to the numerical integration of the Robinson-Trautman equation. This approach eliminates difficulties due to the S2 × R+ topology of the equation. The method is highly accurate for smooth data and is numerically robust. Under spectral decomposition the long-time equilibrium state takes a particularly simple form: all nonlinear (l ≥ 2) modes tend to zero. We discuss the interaction and eventual decay of these higher order modes, as well as the evolution of the Bondi mass and other derived quantities. A qualitative comparison between the Spectral Transform Method and two finite difference schemes is given.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 2 , October 1999 , pp. 271 - 280
Copyright
Copyright © Australian Mathematical Society 1999

References

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