Higher-order force gradient symplectic algorithms. Academic Article uri icon


  • We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 10(3), 10(4), 10(4), and 10(5) better.

published proceedings

  • Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics

author list (cited authors)

  • Chin, S. A., & Kidwell, D. W.

citation count

  • 20

complete list of authors

  • Chin, SA||Kidwell, DW

publication date

  • December 2000