Talk detail

Participant	Bishop, Nigel
Institution	Rhodes University - Department of Mathematics - Grahamstown - Eastern Cape - South Africa

Session	AN4	Accepted	Yes	Order	4	Time	17' + 3'
Talk	Oral abstract	Title	Numerical relativistic null-cone evolutions at $4^{\mbox{th}}$ order accuracy
Co-authors	C Reisswig, NT Bishop and D Pollney
Abstract	Within numerical relativity, the most accurate method available to transport gravitational radiation from a finite worldtube to ${\mathcal I}^+$ is characteristic extraction. In this method, the coordinates are based on radially compactified outgoing null cones, the metric is written in Bondi-Sachs form and is evolved into the future using the vacuum Einstein equations. Existing characteristic codes are only $2^{\mbox{nd}}$ order accurate. Further, because of numerical stability issues, they use a special ``parallelogram'' algorithm for evolution which cannot be extended to higher order. We develop a new approach that uses the method of lines in both the radial and time directions with angular dependence handled pseudo spectrally. The method can, in principle, be applied to any desired order of convergence, and we have implemented and tested the method for stability and convergence at $4^{\mbox{th}}$ order.