Benchmark: Tao's symplectic integration method

Abstract

A benchmark test was conducted for a new symplectic integration method originally developed by Molei Tao. The method raises interest due to its explicit evolution equation, with applicability to both separable and non-separable Hamiltonian systems, and an easy-to-implement, easily generalizable algorithm. In order to compare the method with other, more well-known methods, namely Störmer-Verlet and Runge-Kutta, we conducted a series of benchmark tests comparing their performance in terms of CPU time, system invariants functions conservation, and numerical symplectic area conservation. Overall, it was found that despite being slower than the more optimized Runge-Kutta-Cash-Karp, Tao's method presents a similar performance to Störmer-Verlet, with the extra perk of being more generic and not requiring the use of implicit equations for the evolution of the equations of motion.

20 pages, 3 figures, 7 tables, implementation code