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  <doc>
    <id>844</id>
    <completedYear/>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
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    <completedDate>2005-01-24</completedDate>
    <publishedDate>2005-01-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fast Runge-Kutta approximation of inhomogeneous parabolic equations</title>
    <abstract language="eng">The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\varepsilon$, by solving only $$O\Big(\log N\, \log \frac1\varepsilon \Big) $$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm.</abstract>
    <identifier type="serial">05-10</identifier>
    <identifier type="opus3-id">844</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8443</identifier>
    <enrichment key="SourceTitle">Appeared in: Numer. Math. 102(2005)277-291</enrichment>
    <author>Maria Lopez-Fernandez</author>
    <author>Christian Lubich</author>
    <author>Cesar Palencia</author>
    <author>Achim Schädle</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>parabolic equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Runge-Kutta methods</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65M20">Method of lines</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/844/ZR-05-10.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/844/ZR-05-10.ps</file>
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