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

D. A. Prager, A. W.-C. Lun
1999 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
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 S 2 x 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 (/ > 2) modes tend to zero. We discuss the interaction
more » ... s 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.
doi:10.1017/s0334270000011218 fatcat:zxfh5yttyndrxbknuglxlgkns4