A direct comparison of two codes in numerical relativity

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Abstract
The authors discuss a detailed numerical comparison of the results of two codes which treat the same model problem in numerical relativity. The model consists of a single, massless scalar field minimally coupled to the gravitational field with a further restriction to spherical symmetry. The comparison was complicated by the fact that the codes were based on different formalisms, used different coordinate systems and employed different numerical solution techniques. After briefly reviewing the model and the basic solution methods the authors describe in detail the additional numerical analysis which enabled them to directly (event-by-event) compare their solutions. They also describe some new algorithms which use Richardson extrapolation to significantly increase the accuracy of one of the codes at a given resolution.