## Differential-algebraic Equations: Analysis and Numerical SolutionDifferential-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. |

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asalam o alikum

it is a very googd book on differential algebraic equation.i am also work on this equation.

### Contents

Introduction | 3 |

Linear differentialalgebraic equations with constant coefﬁcients | 13 |

Linear differentialalgebraic equations with variable coefﬁcients | 56 |

Nonlinear differentialalgebraic equations | 151 |

Numerical methods for strangenessfree problems | 217 |

Numerical methods for index reduction | 273 |

Boundary value problems | 298 |

Software for the numerical solution of differentialalgebraic | 352 |

359 | |

373 | |

### Common terms and phrases

algebraic equations analysis apply assume assumptions BDF methods block row boundary value problem characteristic values collocation computation consider consistent initial values constant coefﬁcients control problem convergence corank Corollary corresponding deﬁned Deﬁnition denotes derivative array differential-algebraic equation differentiation index difﬁculties Drazin inverse equivalent Exercise feedback ﬁnally ﬁnd ﬁnite ﬁrst ﬁxed follows Fréchet derivative full row rank given global Hence Hypothesis 3.48 implicit function theorem implies index reduction inﬂated inhomogeneity initial condition initial value problem inverse Jacobian Jordan canonical form kernel l-full Lemma linear differential-algebraic equations linear system manifold matrix pair modiﬁed multi-step method multibody systems nilpotent nodal analysis nonsingular matrix numerical solution obtain ordinary differential equation particular polynomial Proof pseudoinverse Radau reduced differential-algebraic equation reduced problem regular and strangeness-free Runge—Kutta methods satisﬁes Hypothesis 4.2 satisfy Section semi-explicit solve strangeness index sufﬁciently small sufﬁciently smooth Theorem 3.9 transformations unique solution uniquely solvable vector yields