%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}, citeulike-article-id = {13507052}, citeulike-attachment-1 = {rabier_91_geometric_1003408.pdf; /pdf/user/gdmcbain/article/13507052/1003408/rabier_91_geometric_1003408.pdf; c098cd2ac1ab35a053e22651048f831545b69da7}, file = {rabier_91_geometric_1003408.pdf}, howpublished = {Technical Report ICMA-91-162}, institution = {Institute for Computational Mathematics and Applications}, interhash = {94daa87f9d7e79182d6b577baf59d3fa}, 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 }