5 research outputs found
Symmetric multistep methods for constrained Hamiltonian systems
A method of choice for the long-time integration of constrained Hamiltonian systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitrarily high order with a computational cost comparable to that of the Rattle algorith
Line Integral Solution of Hamiltonian Systems with Holonomic Constraints
In this paper, we propose a second-order energy-conserving approximation
procedure for Hamiltonian systems with holonomic constraints. The derivation of
the procedure relies on the use of the so-called line integral framework. We
provide numerical experiments to illustrate theoretical findings.Comment: 30 pages, 3 figures, 4 table
Symmetric multistep methods for constrained Hamiltonian systems
A method of choice for the long-time integration of constrained Hamiltonian systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitrarily high order with a computational cost comparable to that of the Rattle algorithm