Differential-algebraic Equations: Analysis and Numerical Solution
European Mathematical Society, Jan 1, 2006 - Mathematics - 377 pages
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.
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Linear differentialalgebraic equations with constant coefficients
Numerical solution of differentialalgebraic equations
Numerical methods for index reduction
algebraic equations analysis apply assume assumptions BDF methods block row boundary value problem characteristic values collocation collocation methods columns computation consider consistent initial values constant coefficients constraints control problem convergence corank Corollary corresponding defined Definition denotes derivative array differential-algebraic equation differentiation index Drazin inverse equivalent Exercise feedback follows full row rank given global Hence Hypothesis 3.48 implicit function theorem implies index reduction inhomogeneity initial condition initial value problem inverse Jacobian Jordan canonical form kernel Lemma linear differential-algebraic equations linear system manifold matrix pair multi-step method multibody systems nilpotent nodal analysis nonsingular matrix numerical solution obtain ordinary differential equation particular polynomial Proof pseudoinverse reduced differential-algebraic equation reduced problem regular and strangeness-free Runge-Kutta methods satisfies Hypothesis 4.2 Section semi-explicit solve strangeness index sufficiently small sufficiently smooth Theorem 3.9 transformations unique solution uniquely solvable vector x(to yields