Abstract
We present new 6-th and 8-th 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.
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Blanes, S., Casas, F., Ros, J. (2001). New Families of Symplectic Runge-Kutta-Nyström Integration Methods. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_13
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DOI: https://doi.org/10.1007/3-540-45262-1_13
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