English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Time-reversible symplectic methods, which are precisely compatible withLiouville's phase-volume-conservation theorem, are often recommended forcomputational simulations of Hamiltonian mechanics. Lack of energy drift is anapparent advantage of such methods. But all numerical methods are susceptibleto Lyapunov instability, which severely limits the maximum time for whichchaotic solutions can be "accurate". The "advantages" of higher-order methodsare lost rapidly for typical chaotic Hamiltonians. We illustrate thesedifficulties for a useful reproducible test case, the two-dimensionalone-particle cell model with specially smooth forces. This Hamiltonian problemis chaotic and occurs on a three-dimensional constant-energy shell, the minimumdimension for chaos. We benchmark the problem with quadruple-precisiontrajectories using the fourth-order Candy-Rozmus, fifth-order Runge-Kutta, andeighth-order Schlier-Seiter-Teloy integrators. We compare the last,most-accurate particle trajectories to those from six double-precisionalgorithms, four symplectic and two Runge-Kutta.

Comparison of Very Smooth Cell-Model Trajectories Using Five Symplectic and Two Runge-Kutta Integrators