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The main contribution of this paper is to introduce a reconstruction technique that preserves the well-balanced property of Godunov's methods. Some numerical experiments are presented to verify in practice the properties of the developed numerical schemes.<\/jats:p>","DOI":"10.1137\/060674879","type":"journal-article","created":{"date-parts":[[2008,3,5]],"date-time":"2008-03-05T19:23:53Z","timestamp":1204745033000},"page":"1012-1039","source":"Crossref","is-referenced-by-count":104,"title":["Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws"],"prefix":"10.1137","volume":"46","author":[{"given":"Manuel","family":"Castro","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos\u00e9 M.","family":"Gallardo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juan A.","family":"L\u00f3pez-Garc\u00cda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carlos","family":"Par\u00e9s","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,3,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7930(01)00013-5"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/fld.846"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750139738X"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7930(94)90004-3"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"F. 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