A Fundamental Theorem on the Structure of Symplectic Integrators

Details A Fundamental Theorem on the Structure of Symplectic Integrators A Fundamental Theorem on the Structure of Symplectic Integrators

2005-11-15

arxiv.org/abs/math-ph/0511051v1

Phys.Lett. A354 (2006) 373-376

Physics

Mathematical Physics

4 pages, no figures

Scientific paper

10.1016/j.physleta.2006.02.004

I show that the basic structure of symplectic integrators is governed by a theorem which states {\it precisely}, how symplectic integrators with positive coefficients cannot be corrected beyond second order. All previous known results can now be derived quantitatively from this theorem. The theorem provided sharp bounds on second-order error coefficients explicitly in terms of factorization coefficients. By saturating these bounds, one can derive fourth-order algorithms analytically with arbitrary numbers of operators.

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