{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:05:06Z","timestamp":1740135906020,"version":"3.37.3"},"reference-count":0,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":396,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["MA 1662\/1- 2"],"award-info":[{"award-number":["MA 1662\/1- 2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["VLSI Design"],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:p>We apply Wigner\u2010transform techniques to the analysis of difference methods for\nSchr\u00f6dinger\u2010type equations in the case of a small Planck constant. In this way we are\nable to obtain sharp conditions on the spatial\u2010temporal grid which guarantee convergence\nfor average values of observables as the Planck constant tends to zero. The\ntheory developed in this paper is <jats:italic>not<\/jats:italic> based on local and global error estimates and does\n<jats:italic>not<\/jats:italic> depend on whether caustics develop or not.<\/jats:p><jats:p>Numerical examples are presented to help interpret the theory.<\/jats:p>","DOI":"10.1155\/1999\/42190","type":"journal-article","created":{"date-parts":[[2007,9,18]],"date-time":"2007-09-18T12:58:21Z","timestamp":1190120301000},"page":"397-413","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Semiclassical Analysis of Discretizationsof Schr\u00f6dinger\u2010type Equations"],"prefix":"10.1155","volume":"9","author":[{"given":"Peter A.","family":"Markowich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paola","family":"Pietra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carsten","family":"Pohl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[1998,12]]},"container-title":["VLSI Design"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/042190.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/1999\/42190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T13:48:29Z","timestamp":1723211309000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/1999\/42190"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,12]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1155\/1999\/42190"],"URL":"https:\/\/doi.org\/10.1155\/1999\/42190","archive":["Portico"],"relation":{},"ISSN":["1065-514X","1563-5171"],"issn-type":[{"type":"print","value":"1065-514X"},{"type":"electronic","value":"1563-5171"}],"subject":[],"published":{"date-parts":[[1998,12]]},"assertion":[{"value":"1997-08-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"1998-12-01","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}