Differential-Algebraic Systems as Differential Equations on Manifolds
Copyright policy )Differential-Algebraic Systems as Differential Equations on Manifolds
Based on the theory of differential equations on manifolds, existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications. Both the autonomous and nonautonomous case are considered. Moreover, a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower-dimensional manifolds. This class includes systems for which the application of ODE-solvers is known to lead to difficulties. Finally, some solution approach based on continuation techniques is outlined.
existence, uniqueness, continuation techniques, Nonlinear ordinary differential equations and systems, Applications of dynamical systems, non-autonomous, Numerical methods for initial value problems involving ordinary differential equations, differential-algebraic equations, manifolds
existence, uniqueness, continuation techniques, Nonlinear ordinary differential equations and systems, Applications of dynamical systems, non-autonomous, Numerical methods for initial value problems involving ordinary differential equations, differential-algebraic equations, manifolds
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