{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T18:09:20Z","timestamp":1791223760654,"version":"4.1.0"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We investigate finite difference schemes which approximate $2\\times 2$ one-dimensional linear dissipative hyperbolic systems. We show that it is possible to introduce some suitable modifications in standard upwinding schemes, which keep into account the long-time behavior of the solutions, to yield numerical approximations which are increasingly accurate for large times when computing small perturbations of stable asymptotic states, respectively, around stationary solutions and in the diffusion (Chapman\u2013Enskog) limit.<\/jats:p>","DOI":"10.1137\/060678373","type":"journal-article","created":{"date-parts":[[2008,2,21]],"date-time":"2008-02-21T18:06:05Z","timestamp":1203617165000},"page":"869-894","source":"Crossref","is-referenced-by-count":17,"title":["Asymptotic High-Order Schemes for $2\\times2$ Dissipative Hyperbolic Systems"],"prefix":"10.1137","volume":"46","author":[{"given":"Denise","family":"Aregba-Driollet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maya","family":"Briani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roberto","family":"Natalini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,2,20]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7930(94)90004-3"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20195"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-01-01371-0"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"F. Bouchut,\n                      Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes for Sources\n                      , Front. Math., Birkh\u00e4user, Basel, 2004.","DOI":"10.1007\/b93802"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2006.v4.n1.a3"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160470602"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0733001"},{"key":"R8","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.57262\/die\/1367846901","volume":"9","author":"Hanouzet B.","year":"1996","journal-title":"Differential Integral Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0893-4983","issn-type":"print"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-003-0257-6"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2001130"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500018308"},{"key":"R12","unstructured":"R. Natalini,\n                      Recent results on hyperbolic relaxation problems\n                      , in Analysis of Systems of Conservation Laws (Aachen, 1997), Chapman & Hall\/CRC, Boca Raton, FL, 1999, pp. 128\u2013198."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/s10092-001-8181-3"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"P. L. Roe,\n                      Upwind differencing schemes for hyperbolic conservation laws with source term\n                      , in Nonlinear Hyperbolic Problems, C. Carasso, P. A. Raviart, and D. Serre, eds., Lecture Notes in Math. 1270, Springer, Berlin, 1987, pp. 41\u201351.","DOI":"10.1007\/BFb0078316"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.14492\/hokmj\/1381757663"},{"key":"R16","unstructured":"F. Tr\u00e8ves,\n                      Basic Linear Partial Differential Equations\n                      , Pure Appl. Math. (Amst.) 62, Academic Press, New York, 1975."},{"key":"R17","unstructured":"G. B. Whitham,\n                      Linear and Nonlinear Waves\n                      , Wiley & Sons, New York, 1974."}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060678373","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:12:10Z","timestamp":1787325130000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060678373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060678373"],"URL":"https:\/\/doi.org\/10.1137\/060678373","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}