{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T22:51:25Z","timestamp":1649199085198},"reference-count":4,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this article we will discuss the Fast Marching Method which was introduced by James A. Sethian to solve some types of nonlinear partial differential equations efficiently. We will show that this method yields the unique solution to an upwind discretization. Furthermore we will present the correct algorithm for the second order case where existence and unicity of the solution will be proven as well.<\/jats:p>","DOI":"10.2478\/s13537-011-0011-3","type":"journal-article","created":{"date-parts":[[2011,5,25]],"date-time":"2011-05-25T05:34:36Z","timestamp":1306301676000},"source":"Crossref","is-referenced-by-count":0,"title":["On correctness of first and second order fast marching method"],"prefix":"10.2478","volume":"1","author":[{"given":"Christoph","family":"Lass","sequence":"first","affiliation":[]}],"member":"374","reference":[{"key":"11_CR1","unstructured":"Lass C., Diploma thesis, Ernst-Moritz-Arndt-Universit\u00e4t Greifswald, Greifswald, Germany, 2010 (in German)"},{"key":"11_CR2","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1073\/pnas.93.4.1591","volume":"93","author":"J.A. Sethian","year":"1996","unstructured":"Sethian J.A., A Fast Marching Level Set Method for Monotonically Advancing Fronts, P NATL ACAD SCI USA, 1996, 93, 1591\u20131595","journal-title":"P NATL ACAD SCI USA"},{"key":"11_CR3","volume-title":"Level Set Methods and Fast Marching Methods","author":"J.A. Sethian","year":"1999","unstructured":"Sethian J.A., Level Set Methods and Fast Marching Methods, 2nd edition, Cambridge University Press, Cambridge, 1999","edition":"2nd edition"},{"key":"11_CR4","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1109\/9.412624","volume":"40","author":"J.N. Tsitsiklis","year":"1995","unstructured":"Tsitsiklis J.N., Efficient Algorithms for Globally Optimal Trajectories, IEEE T AUTOMAT CONTR, 1995, 40, 1528\u20131538","journal-title":"IEEE T AUTOMAT CONTR"}],"container-title":["Open Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.2478\/s13537-011-0011-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.2478\/s13537-011-0011-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.2478\/s13537-011-0011-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T16:19:04Z","timestamp":1614529144000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/s13537-011-0011-3\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,1]]},"references-count":4,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/s13537-011-0011-3","relation":{},"ISSN":["2299-1093"],"issn-type":[{"value":"2299-1093","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1,1]]}}}