Spectral collocation methods for solution of Einstein's equations in null quasi-spherical coordinates

Andrew H. Norton

( Department of Mathematics, Statistics and Computing Science, University of New England, Armidale, NSW 2351, Australia )

Abstract

The spectral methods which are being used to solve Einstein's equations in null quasi-spherical coordinates are described. They include Fast Fourier methods for evaluating derivatives in a uniform grid representation and methods for transforming to and from spin-weighted spherical harmonic representations. In theory, expressions involving spherical harmonics up to any fixed maximum angular momentum L can be routinely manipulated with accuracy depending only on the machine precision. The code we have running uses L=15 or L=31, with no assumed symmetries.