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The scheme employs several novel geometric and numerical techniques, including a geometrically invariant coordinate 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 harmonics; and a spectral preconditioner for solving a class of first-order elliptic systems on S\n                    <jats:sup>2<\/jats:sup>\n                    . 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 10\n                    <jats:sup>5<\/jats:sup>\n                    , until null time z=55M when the coordinate condition breaks down.\n                  <\/jats:p>","DOI":"10.1137\/s1064827599356171","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"917-950","source":"Crossref","is-referenced-by-count":21,"title":["Numerical Methods for the Einstein Equations in Null Quasi-Spherical Coordinates"],"prefix":"10.1137","volume":"22","author":[{"given":"Robert","family":"Bartnik","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew H.","family":"Norton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/03605309708821302"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1080\/03605309708821302"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1214453422"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/14\/8\/017"},{"key":"R5","unstructured":"R. Bartnik,\n                      Einstein equations in the null quasi\u2010spherical gauge: Progress report\n                      , in the Proceedings of the First Australasian Conference on General Relativity and Gravitation, University of Adelaide, 1996, D. Wiltshire, ed., Institute for Theoretical Physics, University of Adelaide, South Australia, 1996, pp. 25\u201338."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1063\/1.532165"},{"key":"R7","unstructured":"Robert Bartnik, Interaction of gravitational waves with a black hole, Internat. Press, Cambridge, MA, 1999, 3\u2013142000d:83076"},{"key":"R8","unstructured":"R. Bartnik and A. H. Norton,\n                      NQS data explorer website\n                      , University of Canberra, 1997, http:\/\/relativity.ise.canberra.edu.au\/."},{"key":"R9","unstructured":"R. Bartnik and A. H. Norton,\n                      Numerical solution of the Einstein equations\n                      , in Computational Techniques and Applications: CTAC97, Proceedings of the Eighth Biennial Conference, University of Adelaide, 1997, J. Noye, M. Teubner, and A. Gill, eds., World Scientific, Singapore, 1998, pp. 91\u201398."},{"key":"R10","unstructured":"R. Bartnik and A. H. Norton,\n                      Geometric Implementation of Spherical Harmonics\n                      , Tech. rep., School of Mathematics and Statistics, University of Canberra, Australia, 1999;"},{"key":"R10","unstructured":"Also available online at http:\/\/gular.canberra.edu.au\/relativity.html."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.57.7235"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.56.6298"},{"key":"R13","unstructured":"N. Bishop, Some aspects of the characteristic initial value problem in numerical relativity, Cambridge Univ. 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W. Hamming,\n                      Digital Filters\n                      , Prentice\u2010Hall, Upper Saddle River, NJ, 1977."},{"key":"R31","unstructured":"S. W. Hawking and G. R. Ellis,\n                      The large\u2010scale structure of spacetime\n                      , Cambridge University Press, Cambridge, UK, 1973."},{"key":"R32","unstructured":"A. C. Hearn,\n                      REDUCE Users Manual, Version 3.6\n                      , RAND Publication CP78, Santa Monica, CA, 1996."},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5782"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1080\/00046973.1973.9648342"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(74)90173-0"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1063\/1.1724257"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1063\/1.1703927"},{"key":"R38","unstructured":"A. H. 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