In this note some stability results are derived for the Douglas splitting method. The relevance of the theoretical results is tested for an advection-reaction equation.<\/p>","DOI":"10.1090\/s0025-5718-98-00914-4","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:28Z","timestamp":1027721668000},"page":"183-190","source":"Crossref","is-referenced-by-count":20,"title":["A note on stability of the Douglas splitting method"],"prefix":"10.1090","volume":"67","author":[{"given":"Willem","family":"Hundsdorfer","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/BF01386295","article-title":"Alternating direction methods for three space variables","volume":"4","author":"Douglas, Jim, Jr.","year":"1962","journal-title":"Numer. Math.","ISSN":"http:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"2","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1007\/BF01386093","article-title":"A general formulation of alternating direction methods. I. Parabolic and hyperbolic problems","volume":"6","author":"Douglas, Jim, Jr.","year":"1964","journal-title":"Numer. Math.","ISSN":"http:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"3","unstructured":"W. Hundsdorfer, Trapezoidal and midpoint splittings for initial-boundary value problems. CWI Report, 1996."},{"key":"4","doi-asserted-by":"crossref","unstructured":"G.I. Marchuk, Splitting and alternating direction methods. Handbook of Numerical Analysis 1 (P.G. Ciarlet. J.L. Lions, eds.), North-Holland, Amsterdam, pp. 197-462, 1990.","DOI":"10.1016\/S1570-8659(05)80035-3"},{"key":"5","series-title":"A Wiley-Interscience Publication","isbn-type":"print","volume-title":"The finite difference method in partial differential equations","author":"Mitchell, Andrew Ronald","year":"1980","ISBN":"http:\/\/id.crossref.org\/isbn\/0471276413"},{"issue":"3","key":"6","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/BF01930993","article-title":"An extension of \ud835\udc34-stability to alternating direction implicit methods","volume":"19","author":"Warming, R. F.","year":"1979","journal-title":"BIT","ISSN":"http:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00914-4\/S0025-5718-98-00914-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00914-4\/S0025-5718-98-00914-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T23:36:54Z","timestamp":1635896214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00914-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"references-count":6,"journal-issue":{"issue":"221","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["S0025-5718-98-00914-4"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-98-00914-4","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998]]}}}