Order 5 symplectic explicit Runge-Kutta Nystrom methods

Lin-yi Chou and P.W. Sharp


Order five symplectic ERKN methods of five stages are known to exist. However,
these methods do not have free parameters with which to minimise the error
coefficients. By adding one derivative evaluation per step, to give either
a six-stage non-FSAL family or a seven-stage FSAL family of methods, two free parameters
become available for the minimisation. This raises the possibility of improving the
efficiency of order five methods despite the extra cost of taking a step.
We perform the minimisation of the two families to obtain an optimal method
and then compare its performance with some published methods on the two-body
problem for a range of eccentricities. These comparisons
along with those based on the error coefficients show the new method is
significantly more efficient than the five-stage methods. The numerical comparisons
also suggest the new methods can be more efficient than some existing methods
of other orders.

symplectic, explicit Runge-Kutta Nystrom, order 5, optimised

Math Review Classification
Primary 65L06

Last Updated
December 13, 1999

9 pages

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