LEADER 03698nam 22004455a 450 001 9910151937903321 005 20091109150325.0 010 $a3037195177 024 70$a10.4171/017 035 $a(CKB)3710000000953796 035 $a(CH-001817-3)36-091109 035 $a(PPN)178155098 035 $a(EXLCZ)993710000000953796 100 $a20091109j20060228 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferential-Algebraic Equations$b[electronic resource] $eAnalysis and Numerical Solution /$fPeter Kunkel, Volker Mehrmann 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2006 210 1$aZu?rich, Switzerland :$cEuropean Mathematical Society,$d[2006] 215 $a1 online resource (385 pages) 225 0 $aEMS Textbooks in Mathematics (ETB) 320 $aIncludes bibliographical references (pages 359-371) and index. 327 $g1.$tIntroduction --$g2.$tLinear differential-algebraic equations with constant coefficients --$g3.$tLinear differential-algebraic equations with variable coefficients --$g4.$tNonlinear differential-algebraic equations --$g5.$tNumerical methods for strangeness-free problems --$g6.$tNumerical methods for index reduction --$g7.$tBoundary value problems --$g8.$tSoftware for the numerical solution of differential-algebraic equations. 330 $aDifferential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge--Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study. 410 0$aEMS textbooks in mathematics. 606 $aDifferential-algebraic equations$9lat$2NLI 606 $aBoundary value problems$9lat$2NLI 615 7$aDifferential-algebraic equations. 615 7$aBoundary value problems. 686 $a34-xx$a65-xx$2msc 700 $aKunkel$b Peter$0471668 702 $aMehrmann$b V. L$g(Volker Ludwig),$f1955- 801 0$bch0018173 906 $aBOOK 912 $a9910151937903321 996 $aDifferential-Algebraic Equations$92566819 997 $aUNINA