{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T23:24:46Z","timestamp":1748820286494},"reference-count":8,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T00:00:00Z","timestamp":1531353600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We analyze a second-order accurate finite difference method for a spatially periodic convection-diffusion problem. The method is a time stepping method based on the Strang splitting of the spatially semidiscrete solution, in which the diffusion part uses the Crank\u2013Nicolson method and the convection part the explicit forward Euler approximation on a shorter time interval. When the diffusion coefficient is small, the forward Euler method may be used also for the diffusion term.<\/jats:p>","DOI":"10.1515\/cmam-2018-0018","type":"journal-article","created":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T11:10:33Z","timestamp":1531393833000},"page":"283-293","source":"Crossref","is-referenced-by-count":5,"title":["An Explicit-Implicit Splitting Method for a Convection-Diffusion Problem"],"prefix":"10.1515","volume":"19","author":[{"given":"Vidar","family":"Thom\u00e9e","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences , Chalmers University of Technology and University of Gothenburg , SE-412 96 Gothenburg , Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.\u2009S.","family":"Vasudeva Murthy","sequence":"additional","affiliation":[{"name":"TIFR Centre for Applicable Mathematics , Yelahanka New Town , Bangalore 560 065 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,7,12]]},"reference":[{"key":"2023033110022015785_j_cmam-2018-0018_ref_001_w2aab3b7e2295b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"M.  Baldauf,\nLinear stability analysis of Runge\u2013Kutta-based partial time-splitting schemes for the Euler equations,\nMonthly Weather Rev. 138 (2010), 4475\u20134496.","DOI":"10.1175\/2010MWR3355.1"},{"key":"2023033110022015785_j_cmam-2018-0018_ref_002_w2aab3b7e2295b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"D.  Estep, V.  Ginting, D.  Ropp, J. N.  Shadid and S.  Tavener,\nAn a posteriori-a priori analysis of multiscale operator splitting,\nSIAM J. Numer. Anal. 46 (2008), no. 3, 1116\u20131146.","DOI":"10.1137\/07068237X"},{"key":"2023033110022015785_j_cmam-2018-0018_ref_003_w2aab3b7e2295b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"A.  Gassmann and H.-J.  Herzog,\nA consistent time-split numerical scheme applied to the nonhydrostatic compressible equations,\nMonthly Weather Rev. 135 (2007), 20\u201336.","DOI":"10.1175\/MWR3275.1"},{"key":"2023033110022015785_j_cmam-2018-0018_ref_004_w2aab3b7e2295b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"E.  Hansen and A.  Ostermann,\nExponential splitting for unbounded operators,\nMath. Comp. 78 (2009), no. 267, 1485\u20131496.","DOI":"10.1090\/S0025-5718-09-02213-3"},{"key":"2023033110022015785_j_cmam-2018-0018_ref_005_w2aab3b7e2295b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"W.  Hundsdorfer and J.  Verwer,\nNumerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations,\nSpringer Ser. Comput. Math. 33,\nSpringer, Berlin, 2003.","DOI":"10.1007\/978-3-662-09017-6"},{"key":"2023033110022015785_j_cmam-2018-0018_ref_006_w2aab3b7e2295b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"T.  Jahnke and C.  Lubich,\nError bounds for exponential operator splittings,\nBIT 40 (2000), no. 4, 735\u2013744.","DOI":"10.1023\/A:1022396519656"},{"key":"2023033110022015785_j_cmam-2018-0018_ref_007_w2aab3b7e2295b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"S.  MacNamara and G.  Strang,\nOperator splitting,\nSplitting Methods in Communication, Imaging, Science, and Engineering,\nSci. Comput.,\nSpringer, Cham (2016), 95\u2013114.","DOI":"10.1007\/978-3-319-41589-5_3"},{"key":"2023033110022015785_j_cmam-2018-0018_ref_008_w2aab3b7e2295b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"G.  Strang,\nOn the construction and comparison of difference schemes,\nSIAM J. Numer. Anal. 5 (1968), 506\u2013517.","DOI":"10.1137\/0705041"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/19\/2\/article-p283.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0018\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0018\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T10:46:00Z","timestamp":1680259560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0018\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,12]]},"references-count":8,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2,24]]},"published-print":{"date-parts":[[2019,4,1]]}},"alternative-id":["10.1515\/cmam-2018-0018"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2018-0018","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2018,7,12]]}}}