{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:04Z","timestamp":1776728284725,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"238","license":[{"start":{"date-parts":[[2002,12,5]],"date-time":"2002-12-05T00:00:00Z","timestamp":1039046400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    When integrating regular ordinary differential equations numerically, one tries to match carefully the dynamics of the numerical algorithm with the dynamical behaviour of the true solution. The present paper deals with linear index-\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2\">\n                        <mml:semantics>\n                          <mml:mn>2<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    differential-algebraic systems. It is shown how knowledge pertaining to (numerical) regular ordinary differential equations applies provided a certain subspace which is closely related to the tangent space of the constraint manifold remains invariant.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01408-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"605-632","source":"Crossref","is-referenced-by-count":7,"title":["Analyzing the stability behaviour of solutions and their approximations in case of index-2 differential-algebraic systems"],"prefix":"10.1090","volume":"71","author":[{"given":"Roswitha","family":"M\u00e4rz","sequence":"first","affiliation":[]},{"given":"Antonio","family":"Rodr\u00edguez-Santiesteban","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,12,5]]},"reference":[{"key":"1","isbn-type":"print","volume-title":"Numerical solution of initial value problems in differential-algebraic equations","author":"Brenan, K. E.","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0444015116"},{"key":"2","isbn-type":"print","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1017\/s0962492900002269","article-title":"Numerical methods for differential algebraic equations","author":"M\u00e4rz, Roswitha","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0521410266"},{"key":"3","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","volume-title":"Solving ordinary differential equations. I","volume":"8","author":"Hairer, E.","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540566708","edition":"2"},{"key":"4","series-title":"Teubner-Texte zur Mathematik [Teubner Texts in Mathematics]","isbn-type":"print","volume-title":"Differential-algebraic equations and their numerical treatment","volume":"88","author":"Griepentrog, Eberhard","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/3322003434"},{"key":"5","unstructured":"M. Hanke and R. M\u00e4rz: On the asymptotics in the case of differential-algebraic equations. Talk given in Oberwolfach, October 1995."},{"issue":"2-3","key":"6","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0096-3003(97)10041-8","article-title":"An efficient approach for the numerical simulation of multibody systems","volume":"92","author":"Sudarsan, R.","year":"1998","journal-title":"Appl. Math. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0096-3003","issn-type":"print"},{"key":"7","doi-asserted-by":"crossref","unstructured":"D. Est\u00e9vez Schwarz and C. Tischendorf: Structural analysis for electric circuits and consequences for MNA. Intern. J. of Circuit Theory and Applications 18, 131-162, 2000.","DOI":"10.1002\/(SICI)1097-007X(200003\/04)28:2<131::AID-CTA100>3.0.CO;2-W"},{"issue":"1-2","key":"8","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/BF03322452","article-title":"Index-2 differential-algebraic equations","volume":"15","author":"M\u00e4rz, Roswitha","year":"1989","journal-title":"Results Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0378-6218","issn-type":"print"},{"key":"9","series-title":"CWI Monographs","isbn-type":"print","volume-title":"Stability of Runge-Kutta methods for stiff nonlinear differential equations","volume":"2","author":"Dekker, K.","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0444876340"},{"issue":"3","key":"10","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1137\/S0895479897325955","article-title":"Logarithmic norms for matrix pencils","volume":"20","author":"Higueras, Inmaculada","year":"1999","journal-title":"SIAM J. Matrix Anal. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4798","issn-type":"print"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1137\/0723054","article-title":"Order results for implicit Runge-Kutta methods applied to differential\/algebraic systems","volume":"23","author":"Petzold, L. R.","year":"1986","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"12","unstructured":"E. Izquierdo Macana: Numerische Approximation von Algebro-Differentialgleichungen mit Index 2 mittels impliziter Runge-Kutta-Verfahren. Doctoral thesis, Humboldt-Univ., Fachbereich Mathematik, Berlin, 1993."},{"issue":"4","key":"13","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1137\/0728059","article-title":"Projected implicit Runge-Kutta methods for differential-algebraic equations","volume":"28","author":"Ascher, Uri M.","year":"1991","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01408-9\/S0025-5718-01-01408-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01408-9\/S0025-5718-01-01408-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:56:37Z","timestamp":1776725797000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01408-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,12,5]]},"references-count":13,"journal-issue":{"issue":"238","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["S0025-5718-01-01408-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01408-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2001,12,5]]}}}