A Geometric Treatment of Implicit Differential-Algebraic Equations
P. Rabier, and W. Rheinboldt. Institute for Computational Mathematics and Applications, (May 1991)
Abstract
A differential--geometric approach for proving the existence and uniqueness of solutions of implicit differential--algebraic equations is presented. It provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems. The differential--algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of tangent bundles here called reducible \$\pi\$-submanifolds. Local existence and uniqueness results for differential--algebraic equations then follow directly from the final stage of this reduction by means of an application of the standard theory of ordinary differential equations.
%0 Report
%1 citeulike:13507052
%A Rabier, Patrick J.
%A Rheinboldt, Werner C.
%D 1991
%I Department of Mathematics and Statistics, University of Pittsburgh
%K 15a22-matrix-pencils 34a09-implicit-odes-daes
%T A Geometric Treatment of Implicit Differential-Algebraic Equations
%X A differential--geometric approach for proving the existence and uniqueness of solutions of implicit differential--algebraic equations is presented. It provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems. The differential--algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of tangent bundles here called reducible \$\pi\$-submanifolds. Local existence and uniqueness results for differential--algebraic equations then follow directly from the final stage of this reduction by means of an application of the standard theory of ordinary differential equations.
@techreport{citeulike:13507052,
abstract = {{A differential--geometric approach for proving the existence and uniqueness of solutions of implicit differential--algebraic equations is presented. It provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems. The differential--algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of tangent bundles here called reducible \$\pi\$-submanifolds. Local existence and uniqueness results for differential--algebraic equations then follow directly from the final stage of this reduction by means of an application of the standard theory of ordinary differential equations.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Rabier, Patrick J. and Rheinboldt, Werner C.},
biburl = {https://www.bibsonomy.org/bibtex/2deeb43ebd0e4b9a21c22d2d1bc1dbf55/gdmcbain},
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file = {rabier_91_geometric_1003408.pdf},
howpublished = {Technical Report ICMA-91-162},
institution = {Institute for Computational Mathematics and Applications},
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intrahash = {deeb43ebd0e4b9a21c22d2d1bc1dbf55},
keywords = {15a22-matrix-pencils 34a09-implicit-odes-daes},
month = may,
posted-at = {2015-02-02 22:28:38},
priority = {3},
publisher = {Department of Mathematics and Statistics, University of Pittsburgh},
timestamp = {2022-05-20T04:25:34.000+0200},
title = {{A Geometric Treatment of Implicit Differential-Algebraic Equations}},
year = 1991
}