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    <id>843</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-01-24</completedDate>
    <publishedDate>2005-01-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fast and oblivious convolution quadrature</title>
    <abstract language="eng">We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N\, \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the convolution kernel, but instead $O(\log N)$ evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation with transparent boundary conditions.</abstract>
    <identifier type="serial">05-09</identifier>
    <identifier type="opus3-id">843</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8437</identifier>
    <enrichment key="SourceTitle">Appeared in:SIAM J. Sci. Comput. Vol. 28(2) (2005) 421-438</enrichment>
    <author>Achim Schädle</author>
    <author>Maria Lopez-Fernandez</author>
    <author>Christian Lubich</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convolution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>numerical integration</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Runge-Kutta methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Volterra integral equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>anomalous diffusion</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65R20">Integral equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/843/ZR-05-09.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/843/ZR-05-09.pdf</file>
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