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  <doc>
    <id>1033</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-11-09</completedDate>
    <publishedDate>2007-11-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Review of Transparent and Artificial Boundary Conditions Techniques  for Linear and Nonlinear Schrödinger Equations</title>
    <abstract language="eng">In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.</abstract>
    <identifier type="serial">07-34</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1061</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10332</identifier>
    <enrichment key="SourceTitle">Appeared in: Commun. Comput. Phys. 4 (2008), 729-796</enrichment>
    <author>Xavier Antoine</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Arnold</author>
    <author>Christophe Besse</author>
    <author>Matthias Ehrhardt</author>
    <author>Achim Schädle</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-34</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schrödinger equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete convolution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>unbounded domain</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="pacs" number="02.70.Bf">Finite-difference methods</collection>
    <collection role="msc" number="35Q40">PDEs in connection with quantum mechanics</collection>
    <collection role="msc" number="45K05">Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]</collection>
    <collection role="msc" number="65M12">Stability and convergence of numerical methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1033/ZR_07_34.pdf</file>
  </doc>
</export-example>
