Document Zbl 0937.34059

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Numer. Math.</a> <a href="/?q=in%3A58085" title="Articles in this Issue">27, No. 3, 309-325 (1998)</a>. </div> <div class="abstract">Summary: The authors prove that for Hessenberg delay DAEs of retarded type the direct linearization along the stationary solution is valid. This validity is obtained by showing the equivalence between the direct linearization and the linearization of the state space form of the original problem, which is assured to be legitimate. Thus the study of the asymptotic stability of the stationary solution can be transformed to the study of the null solution of the linearization of the original problem. The authors point out that a similar method can be used to prove the validity of the direct linearization of delay differential-algebraic equations of neutral type.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1311238">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34K20" title="MSC2020">34K20</a> </td> <td class="space"> Stability theory of functional-differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A09" title="MSC2020">34A09</a> </td> <td class="space"> Implicit ordinary differential equations, differential-algebraic equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L80" title="MSC2020">65L80</a> </td> <td class="space"> Numerical methods for differential-algebraic equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aasymptotic+stability">asymptotic stability</a>; <a href="/?q=ut%3AHessenberg+delay">Hessenberg delay</a>; <a href="/?q=ut%3Adifferential-algebraic+equations">differential-algebraic equations</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0937.34059" data-ciurl="/ci/01311238" data-biburl="/bibtex/01311238.bib" data-amsurl="/amsrefs/01311238.bib" data-xmlurl="/xml/01311238.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01311238.pdf" title="Zbl 0937.34059 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/S0168-9274(98)00008-7" aria-label="DOI for “Asymptotic stability of Hessenberg delay differential-algebraic equations of retarded or neutral type”" title="10.1016/S0168-9274(98)00008-7">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ascher, U.; Petzold, L., The numerical solution of delay-differential-algebraic equations of retarded and neutral type, SIAM J. 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J., The stability of a class of Runge-Kutta methods for delay differential equations, Appl. Numer. Math., 9, 347-355 (1992) · <a href="/0749.65048" class="nowrap">Zbl 0749.65048</a></td> </tr><tr> <td>[11]</td> <td class="space">in’t Hout, K. J., The stability of θ-methods for systems of delay differential equations, Ann. Numer. Math., 1, 323-334 (1994) · <a href="/0837.65087" class="nowrap">Zbl 0837.65087</a></td> </tr><tr> <td>[12]</td> <td class="space">in’t Hout, K. 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Math., 49, 305-318 (1986) · <a href="/0598.65056" class="nowrap">Zbl 0598.65056</a></td> </tr><tr> <td>[19]</td> <td class="space">Zennaro, M., Delay differential equations: theory and numerics, Adv. Numer. Anal., 4 (1995) · <a href="/0847.34072" class="nowrap">Zbl 0847.34072</a></td> </tr><tr> <td>[20]</td> <td class="space">Zhu, W.; Petzold, L. R., Asymptotic stability of linear delay differential-algebraic equations and numerical methods, Appl. Numer. Math., 24, 247-264 (1997) · <a href="/0879.65060" class="nowrap">Zbl 0879.65060</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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