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  <doc>
    <id>1069</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-03-10</completedDate>
    <publishedDate>2008-03-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Parametric Solution of Underdetermined linear ODEs</title>
    <abstract language="eng">The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Gr\"{o}bner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible at http://lie.math.brocku.ca/crack/uode.</abstract>
    <identifier type="serial">08-15</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1098</identifier>
    <identifier type="doi">10.1134/S0361768811020113</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10693</identifier>
    <enrichment key="SourceTitle">Appeared in: Programming and Computer Software, 37 (2011), Number 2, pp. 62-70</enrichment>
    <author>Thomas Wolf</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>08-15</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear ODEs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>underdetermined systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Euclid's algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>computer algebra</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Reduce</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Crack</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="pacs" number="02.30.Hq">Ordinary differential equations</collection>
    <collection role="pacs" number="02.70.Wz">Symbolic computation (computer algebra)</collection>
    <collection role="msc" number="34H05">Control problems [See also 49J15, 49K15, 93C15]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1069/ZR_08_15.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1069/ZR_08_15.ps</file>
  </doc>
</export-example>
