Stability of velocity-Verlet- and Liouville-operator-derived algorithms to integrate non-Hamiltonian systems

研究成果: Article査読

5 被引用数 (Scopus)

抄録

We investigate the difference between the velocity Verlet and the Liouville-operator-derived (LOD) algorithms by studying two non-Hamiltonian systems, one dissipative and the other conservative, for which the Jacobian of the transformation can be determined exactly. For the two systems, we demonstrate that (1) the velocity Verlet scheme fails to integrate the former system while the first- and second-order LOD schemes succeed and (2) some first-order LOD fails to integrate the latter system while the velocity Verlet and the other first- and second-order schemes succeed. We have shown that the LOD schemes are stable for the former system by determining the explicit forms of the shadow Hamiltonians which are exactly conserved by the schemes. We have shown that the Jacobian of the velocity Verlet scheme for the former system and that of the first-order LOD scheme for the latter system are always smaller than the exact values, and therefore, the schemes are unstable. The decomposition-order dependence of LOD schemes is also considered.

本文言語English
論文番号154101
ジャーナルJournal of Chemical Physics
149
15
DOI
出版ステータスPublished - 2018 10月 21
外部発表はい

ASJC Scopus subject areas

  • 物理学および天文学(全般)
  • 物理化学および理論化学

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