New families of symplectic Runge-Kutta-Nyström integration methods. (English) Zbl 0978.65119
Vulkov, Lubin (ed.) et al., Numerical analysis and its applications. 2nd international conference, NAA 2000, Rousse, Bulgaria, June 11-15, 2000. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 1988, 102-109 (2001).
Summary: We present new 6th- and 8th-order explicit symplectic Runge-Kutta-Nyström methods for Hamiltonian systems which are more efficient than other previously known algorithms. The methods use the processing technique and non-trivial flows associated with different elements of the Lie algebra involved in the problem. Both the processor and the kernel are compositions of explicitly computable maps.
For the entire collection see [Zbl 0958.00035].
For the entire collection see [Zbl 0958.00035].
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
