NUMERICAL METHODS FOR THE EINSTEIN EQUATIONS IN NULL QUASI-SPHERICAL COORDINATES.

We describe algorithms used in our construction of a fourth-order in time evolution for the full Einstein equations and assess the accuracy of some representative solutions. The scheme employs several novel geometric and numerical techniques, including a geometrically invariant co- ordinate gauge, which leads to a characteristic-transport formulation of the underlying hyperbolic system, combined with a ‘method of lines’ evolution; convolution splines for radial interpolation, regridding, differentiation, and noise suppression; representations using spin-weighted spherical har- monics; and a spectral preconditioner for solving a class of first-order elliptic systems on S². Initial data for the evolution is unconstrained, subject only to a mild size condition. For sample initial data of ‘intermediate’ strength (19% of the total mass in gravitational energy), the code is accurate to 1 part in 105, until null time z = 55m when the coordinate condition breaks down. [ABSTRACT FROM AUTHOR]