A direct comparison of two codes in numerical relativity

AbsIraeL We discuss a detailed numerical comparison of the results of two mdes which treat lhe same model problem in numerical relativity. m e 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 our basic solution methods we describe in detail the additional numerical analysis which enabled us to directly (evenl-by-event) compare our solutions. We also describe some new algorithms which use Richardson entraplation to significantly increase the accuracy of one of the mdes at a given resolution. Using the basic methodology of convergence testing, and with the aid of high-accuracy (better than 0.001%) numerical results (alw generated using extrapolation techniques), we find clear evidence that both mdes are convergent men in the regime where the field interactions are significantly non-linear and highly time-dependent. We suggesl that techniques such as those described in this paper will be very useful for testing mdes which solve more general problems in numerical relativity. 1.