Holdings: Differential-algebraic equations

Differential-algebraic equations: analysis and numerical solution

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Bibliographic Details
Main Authors:	Kunkel, Peter (Author), Mehrmann, Volker (Author)
Format:	Book
Language:	English
Published:	Zürich European Math. Soc. 2006
Series:	EMS textbooks in mathematics
Subjects:	Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System Differential-algebraisches Gleichungssystem Numerisches Verfahren
Online Access:	Inhaltsverzeichnis
Physical Description:	VIII, 377 S.
ISBN:	3037190175

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MARC


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Record in the Search Index

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adam_text	Contents I Analysis of differential-algebraic equations 1 1 Introduction 3 1.1 Solvability concepts . 5 1.2 Index concepts . 6 1.3 Applications . 8 1.4 How to use this book in teaching . 11 2 Linear differential-algebraic equations with constant coefficients 13 2.1 Canonical forms . 13 2.2 The Drazin inverse . 22 2.3 Explicit representation of solutions . 27 2.4 Generalized solutions . 32 2.5 Control problems . 48 Bibliographical remarks . 52 Exercises . 53 3 Linear differential-algebraic equations with variable coefficients 56 3.1 Canonical forms . 56 3.2 Local and global invariants . 80 3.3 The differentiation index . 96 3.4 Differential-algebraic operators and generalized inverses . 114 3.5 Generalized solutions . 132 3.6 Control problems . 138 Bibliographical remarks . 147 Exercises . 147 4 Nonlinear differential-algebraic equations 151 4.1 Existence and uniqueness of solutions . 151 4.2 Structured problems . 167 4.3 Over-and underdetermined problems . 182 4.4 Control problems . 189 4.5 Differential equations on manifolds . 195 Bibliographical remarks . 210 Exercises . 210 viii Contents II Numerical solution of differential-algebraic equations 215 5 Numerical methods for strangeness-free problems 217 5.1 Preparations . 218 5.2 One-step methods . 224 5.3 Multi-step methods . 254 Bibliographical remarks . 270 Exercises . 270 6 Numerical methods for index reduction 273 6.1 Index reduction for linear problems . 274 6.2 Index reduction for nonlinear problems . 279 6.3 Index reduction via feedback control . 284 6.4 Index reduction by minimal extension . 286 Bibliographical remarks . 295 Exercises . 295 7 Boundary value problems 298 7.1 Existence and uniqueness of solutions . 299 7.2 Multiple shooting . 304 7.3 Collocation . 314 Bibliographical remarks . 348 Exercises . 348 8 Software for the numerical solution of differential-algebraic equations 352 Bibliographical remarks . 355 Exercises . 355 Final remarks 357 Bibliography 359 Index 373
adam_txt	Contents I Analysis of differential-algebraic equations 1 1 Introduction 3 1.1 Solvability concepts . 5 1.2 Index concepts . 6 1.3 Applications . 8 1.4 How to use this book in teaching . 11 2 Linear differential-algebraic equations with constant coefficients 13 2.1 Canonical forms . 13 2.2 The Drazin inverse . 22 2.3 Explicit representation of solutions . 27 2.4 Generalized solutions . 32 2.5 Control problems . 48 Bibliographical remarks . 52 Exercises . 53 3 Linear differential-algebraic equations with variable coefficients 56 3.1 Canonical forms . 56 3.2 Local and global invariants . 80 3.3 The differentiation index . 96 3.4 Differential-algebraic operators and generalized inverses . 114 3.5 Generalized solutions . 132 3.6 Control problems . 138 Bibliographical remarks . 147 Exercises . 147 4 Nonlinear differential-algebraic equations 151 4.1 Existence and uniqueness of solutions . 151 4.2 Structured problems . 167 4.3 Over-and underdetermined problems . 182 4.4 Control problems . 189 4.5 Differential equations on manifolds . 195 Bibliographical remarks . 210 Exercises . 210 viii Contents II Numerical solution of differential-algebraic equations 215 5 Numerical methods for strangeness-free problems 217 5.1 Preparations . 218 5.2 One-step methods . 224 5.3 Multi-step methods . 254 Bibliographical remarks . 270 Exercises . 270 6 Numerical methods for index reduction 273 6.1 Index reduction for linear problems . 274 6.2 Index reduction for nonlinear problems . 279 6.3 Index reduction via feedback control . 284 6.4 Index reduction by minimal extension . 286 Bibliographical remarks . 295 Exercises . 295 7 Boundary value problems 298 7.1 Existence and uniqueness of solutions . 299 7.2 Multiple shooting . 304 7.3 Collocation . 314 Bibliographical remarks . 348 Exercises . 348 8 Software for the numerical solution of differential-algebraic equations 352 Bibliographical remarks . 355 Exercises . 355 Final remarks 357 Bibliography 359 Index 373
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spelling	Kunkel, Peter Verfasser aut Differential-algebraic equations analysis and numerical solution Peter Kunkel ; Volker Mehrmann Differential algebraic equations Zürich European Math. Soc. 2006 VIII, 377 S. txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System (DE-588)4013396-5 gnd rswk-swf Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s Dynamisches System (DE-588)4013396-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Mehrmann, Volker Verfasser aut Erscheint auch als Kunkel, Peter Differential-algebraic equations 978-3-03719-517-8 (DE-604)BV036713192 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014712081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Kunkel, Peter Mehrmann, Volker Differential-algebraic equations analysis and numerical solution Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System (DE-588)4013396-5 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
subject_GND	(DE-588)4013396-5 (DE-588)4229517-8 (DE-588)4128130-5
title	Differential-algebraic equations analysis and numerical solution
title_alt	Differential algebraic equations
title_auth	Differential-algebraic equations analysis and numerical solution
title_exact_search	Differential-algebraic equations analysis and numerical solution
title_exact_search_txtP	Differential-algebraic equations analysis and numerical solution
title_full	Differential-algebraic equations analysis and numerical solution Peter Kunkel ; Volker Mehrmann
title_fullStr	Differential-algebraic equations analysis and numerical solution Peter Kunkel ; Volker Mehrmann
title_full_unstemmed	Differential-algebraic equations analysis and numerical solution Peter Kunkel ; Volker Mehrmann
title_short	Differential-algebraic equations
title_sort	differential algebraic equations analysis and numerical solution
title_sub	analysis and numerical solution
topic	Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System (DE-588)4013396-5 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
topic_facet	Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System Differential-algebraisches Gleichungssystem Numerisches Verfahren
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014712081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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