{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T08:51:51Z","timestamp":1759827111294,"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\/1-3"],"award-info":[{"award-number":["MA 1662\/1-3"]}],"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>Transparent boundary conditions (TBCs) for general Schr\u00f6dinger\u2010type equations on a\nbounded domain can be derived explicitly under the assumption that the given potential\n<jats:italic>V<\/jats:italic>  is constant on the exterior of that domain. In 1D these boundary conditions are non\u2010local\nin time (of memory type).<\/jats:p><jats:p>Existing discretizations of these TBCs have accuracy problems and render the overall\nCrank\u2013Nicolson finite difference method only conditionally stable. In this paper a\nnovel discrete TBC is derived directly from the discrete whole\u2010space problem that yields\nan unconditionally stable scheme. Numerical examples illustrate the superiority of the\ndiscrete TBC over other existing consistent discretizations of the differential TBCs.<\/jats:p><jats:p>As an application of these boundary conditions to wave propagation problems in\nunderwater acoustics results for the so\u2010called standard and wide angle \u201cparabolic\u201d\nequation (SPE, WAPE) models are presented.<\/jats:p>","DOI":"10.1155\/1999\/72984","type":"journal-article","created":{"date-parts":[[2007,9,18]],"date-time":"2007-09-18T12:58:21Z","timestamp":1190120301000},"page":"325-338","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Discrete Transparent Boundary Conditions for GeneralSchr\u00f6dinger\u2010type Equations"],"prefix":"10.1155","volume":"9","author":[{"given":"Matthias","family":"Ehrhardt","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[1998,12]]},"container-title":["VLSI Design"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/072984.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/1999\/72984","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T13:48:14Z","timestamp":1723211294000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/1999\/72984"}},"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\/72984"],"URL":"https:\/\/doi.org\/10.1155\/1999\/72984","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":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"1998-12-01","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}