{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T16:51:00Z","timestamp":1789836660664,"version":"4.0.1"},"reference-count":7,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>In this paper, we present and analyze a new finite difference method for computing three-dimensional wave maps into spheres. By introducing the angular momentum as an auxiliary variable, we recast the governing equation as a first order system. For this new system, we propose a discretization that conserves both the energy and the length constraint. The new method is also fast, requiring only $N\\log N$ operations at each time step. Our main result is that the method converges to a weak solution as discretization parameters go to zero. The paper is concluded by numerical experiments demonstrating convergence of the method and its ability to predict finite time blow-up.<\/jats:p>","DOI":"10.1137\/130948823","type":"journal-article","created":{"date-parts":[[2014,8,19]],"date-time":"2014-08-19T13:33:47Z","timestamp":1408455227000},"page":"2073-2091","source":"Crossref","is-referenced-by-count":8,"title":["A New Angular Momentum Method for Computing Wave Maps into Spheres"],"prefix":"10.1137","volume":"52","author":[{"given":"Trygve K.","family":"Karper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Franziska","family":"Weber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,8,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-009-0282-y"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/080731475"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/060659971"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-09-02221-2"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-02026-1"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/050631070"},{"key":"atypb7","volume-title":"Courant Lect. Notes Math. 2","author":"Shatah J.","year":"1998"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130948823","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:53:12Z","timestamp":1787334792000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130948823"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1137\/130948823"],"URL":"https:\/\/doi.org\/10.1137\/130948823","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}