The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients

Details The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients

2005-11-08

arxiv.org/abs/math-ph/0511031v2

Phys.Rev. E73 (2006) 026705

Physics

Mathematical Physics

12 pages, 2 figures, submitted to Phys. Rev. E, corrected typos

Scientific paper

10.1103/PhysRevE.73.026705

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these {\it extended-linear} symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forward fourth-order algorithms with arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.

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