RATTLE Method for Dissipative Constrained Hamiltonian Systems
ICIRA '08 Proceedings of the First International Conference on Intelligent Robotics and Applications: Part I
Linear Stability of Partitioned Runge-Kutta Methods
SIAM Journal on Numerical Analysis
Variational collision integrator for polymer chains
Journal of Computational Physics
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We consider a general class of systems of overdetermined differential-algebraic equations (ODAEs). We are particularly interested in extending the application of the symplectic Gauss methods to Hamiltonian and Lagrangian systems with holonomic constraints. For the numerical approximation to the solution to these ODAEs, we present specialized partitioned additive Runge-Kutta (SPARK) methods, and in particular the new class of $(s,s)$-Gauss-Lobatto SPARK methods. These methods not only preserve the constraints, symmetry, symplecticness of the flow, and variational nature of the trajectories of holonomically constrained Hamiltonian and Lagrangian systems, but they also have an optimal order of convergence $2s$. A corrected version of this article has been appended at the end of the pdf file.