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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 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 interactiondoi:10.1017/s0334270000011218 fatcat:zxfh5yttyndrxbknuglxlgkns4