{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:38:05Z","timestamp":1776793085440,"version":"3.51.2"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"273","license":[{"start":{"date-parts":[[2011,4,23]],"date-time":"2011-04-23T00:00:00Z","timestamp":1303516800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We develop a simple energy method for proving the stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. In particular, we extend to several space dimensions and to variable coefficients a crucial stability result by Goldberg and Tadmor for Dirichlet boundary conditions. This allows us to give some conditions on the discretized operator that ensure that stability estimates for zero initial data imply a semigroup stability estimate for general initial data. We apply this criterion to several numerical schemes in two space dimensions.<\/p>","DOI":"10.1090\/s0025-5718-10-02368-9","type":"journal-article","created":{"date-parts":[[2010,10,4]],"date-time":"2010-10-04T11:01:54Z","timestamp":1286190114000},"page":"165-203","source":"Crossref","is-referenced-by-count":11,"title":["Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems"],"prefix":"10.1090","volume":"80","author":[{"given":"Jean-Fran\u00e7ois","family":"Coulombel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antoine","family":"Gloria","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2010,4,23]]},"reference":[{"key":"1","series-title":"Oxford Mathematical Monographs","isbn-type":"print","volume-title":"Multidimensional hyperbolic partial differential equations","author":"Benzoni-Gavage, Sylvie","year":"2007","ISBN":"https:\/\/id.crossref.org\/isbn\/9780199211234"},{"issue":"154","key":"2","doi-asserted-by":"publisher","first-page":"603","DOI":"10.2307\/2007665","article-title":"Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II","volume":"36","author":"Goldberg, Moshe","year":"1981","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"3","series-title":"Pure and Applied Mathematics (New York)","isbn-type":"print","volume-title":"Time dependent problems and difference methods","author":"Gustafsson, Bertil","year":"1995","ISBN":"https:\/\/id.crossref.org\/isbn\/0471507342"},{"key":"4","doi-asserted-by":"publisher","first-page":"649","DOI":"10.2307\/2005093","article-title":"Stability theory of difference approximations for mixed initial boundary value problems. II","volume":"26","author":"Gustafsson, Bertil","year":"1972","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"5","doi-asserted-by":"publisher","first-page":"163","DOI":"10.2307\/2315890","article-title":"A formula for the spectral radius of an operator","volume":"75","author":"Holmes, R. B.","year":"1968","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"key":"6","first-page":"51","article-title":"Difference approximations for hyperbolic differential equations","author":"Kreiss, Heinz-Otto","year":"1966"},{"key":"7","doi-asserted-by":"publisher","first-page":"703","DOI":"10.2307\/2004572","article-title":"Stability theory for difference approximations of mixed initial boundary value problems. I","volume":"22","author":"Kreiss, Heinz-Otto","year":"1968","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1002\/cpa.3160230304","article-title":"Initial boundary value problems for hyperbolic systems","volume":"23","author":"Kreiss, Heinz-Otto","year":"1970","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"key":"9","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1002\/cpa.3160170311","article-title":"Difference schemes for hyperbolic equations with high order of accuracy","volume":"17","author":"Lax, Peter D.","year":"1964","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"key":"10","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1002\/cpa.3160190409","article-title":"On stability for difference schemes: A sharp form of G\u0227rding\u2019s inequality","volume":"19","author":"Lax, P. D.","year":"1966","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"issue":"161","key":"11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/2007362","article-title":"Stability theory of difference approximations for multidimensional initial-boundary value problems","volume":"40","author":"Michelson, Daniel","year":"1983","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"12","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1002\/cpa.3160250305","article-title":"\\cal\ud835\udc3f\u2082 is a continuable initial condition for Kreiss\u2019 mixed problems","volume":"25","author":"Rauch, Jeffrey","year":"1972","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"key":"13","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/0024-3795(86)90016-9","article-title":"Complex symmetric matrices with strongly stable iterates","volume":"78","author":"Tadmor, Eitan","year":"1986","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/0024-3795(77)90025-8","article-title":"Symmetric hyperbolic difference schemes and matrix problems","volume":"16","author":"Turkel, E.","year":"1977","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"key":"15","doi-asserted-by":"publisher","first-page":"767","DOI":"10.2307\/2004611","article-title":"On the stability of Friedrichs\u2019 scheme and the modified Lax-Wendroff scheme","volume":"24","author":"Vaillancourt, R\u00e9mi","year":"1970","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"16","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1137\/0705005","article-title":"Well-posed problems and stable difference operators","volume":"5","author":"Wendroff, Burton","year":"1968","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"209","key":"17","doi-asserted-by":"publisher","first-page":"71","DOI":"10.2307\/2153323","article-title":"The semigroup stability of the difference approximations for initial-boundary value problems","volume":"64","author":"Wu, Lixin","year":"1995","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2011-80-273\/S0025-5718-10-02368-9\/S0025-5718-10-02368-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-273\/S0025-5718-10-02368-9\/S0025-5718-10-02368-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:40:28Z","timestamp":1776789628000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-273\/S0025-5718-10-02368-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,23]]},"references-count":17,"journal-issue":{"issue":"273","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["S0025-5718-10-02368-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-10-02368-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2010,4,23]]}}}