Composition methods in the presence of small parameters

S. Z. Burstein and A. A. Mirin,Third order difference methods for hyperbolic equations, J. Comp. Phys., 5 (1970), pp. 547–571.

I. Gjaja, A. J. Dragt and D. T. Abell,A comparison of methods for long-term tracking using symplectic maps, preprint, Physics Dept., Univ. of Maryland, 1993.

D. Goldman and T. J. Kaper,Nth-order operator splitting schemes and nonreversible systems, Center for Fluid Mechanics Turbulence and Computation publication, pp. 93–16, 1993.

E. Hairer, S. P. Nørsett and G. Wanner,Solving Ordinary Differential Equations I, 2nd ed., Springer-Verlag, Berlin New York, 1993.

P.-V. Koseleff,Relations among formal Lie series and construction of symplectic integrators, in Applied Algebra, Algebraic Algorithms and Error-correcting Codes, AAECC 10 (Puerto Rico, 1993), G. Cohen, T. Mora, and O. Moreno, eds., Springer, Berlin New York, 1993.

R. I. McLachlan,On the numerical integration of ordinary differential equations by symmetric composition methods, SIAM J. Sci. Comp. 16 (1995), pp. 151–168.

P. Saha and S. Tremaine,Symplectic integrators for solar system dynamics, Astron. J., 104 (1992), pp. 1633–1640.

J. Wisdom,The origin of the Kirkwood gaps: a mapping for the asteroidal motion near the 3/1 commensurability, Astron. J., 87 (1982), pp. 577–593.

J. Wisdom and M. Holman,Symplectic maps for the N-body problem, Astron. J., 102 (1991), pp. 1528–1538.

J. Wisdom, M. Holman, and J. Touma,Symplectic correctors, preprint, M.I.T., 1994.

H. Yoshida,Construction of higher order symplectic integrators, Phys. Letters A, 150 (1990), pp. 262–268.