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In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional central weighted ENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multidimensional fifth-order scheme. Our numerical examples in one, two, and three space dimensions verify the expected order of accuracy of the schemes.<\/jats:p>","DOI":"10.1137\/s0036142902408404","type":"journal-article","created":{"date-parts":[[2003,11,7]],"date-time":"2003-11-07T11:19:22Z","timestamp":1068203962000},"page":"1339-1369","source":"Crossref","is-referenced-by-count":56,"title":["High-Order Central WENO Schemes for Multidimensional Hamilton-Jacobi Equations"],"prefix":"10.1137","volume":"41","author":[{"given":"Steve","family":"Bryson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Doron","family":"Levy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199612)49:12<1339::AID-CPA5>3.3.CO;2-N"},{"key":"R2","first-page":"85","volume":"320","author":"Arminjon Paul","year":"1995","journal-title":"C. 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