Volume 20, Issue 6
Structure-Preserving Algorithms for Dynamical Systems

Geng Sun

DOI:

J. Comp. Math., 20 (2002), pp. 619-626

Published online: 2002-12

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  • Abstract

We study structure-preserving algorithms to phase space volume for linear dynamical systems y = Ly for which arbitrarily high order explicit symmetric structure-preserving schemes, i.e. the numerical solutions generated by the schemes satisfy $\det(\frac{\partial y_1}{\partial y_0})=e^{htrL}$, where trL is the trace of matrix L,can be constructed.For nonlinear dynamical systems $\dot{y}=f(y)$ Feng-Shang first-order volume-preserving scheme can be also constructed starting from modified $\theta-$methods and is shown that the scheme is structure-preserving to phase space volume.

  • Keywords

structure-preserving algorithm phase space volume source-free dynamical system

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@Article{JCM-20-619, author = {}, title = {Structure-Preserving Algorithms for Dynamical Systems}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {6}, pages = {619--626}, abstract = { We study structure-preserving algorithms to phase space volume for linear dynamical systems y = Ly for which arbitrarily high order explicit symmetric structure-preserving schemes, i.e. the numerical solutions generated by the schemes satisfy $\det(\frac{\partial y_1}{\partial y_0})=e^{htrL}$, where trL is the trace of matrix L,can be constructed.For nonlinear dynamical systems $\dot{y}=f(y)$ Feng-Shang first-order volume-preserving scheme can be also constructed starting from modified $\theta-$methods and is shown that the scheme is structure-preserving to phase space volume. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8947.html} }
TY - JOUR T1 - Structure-Preserving Algorithms for Dynamical Systems JO - Journal of Computational Mathematics VL - 6 SP - 619 EP - 626 PY - 2002 DA - 2002/12 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8947.html KW - structure-preserving algorithm KW - phase space volume KW - source-free dynamical system AB - We study structure-preserving algorithms to phase space volume for linear dynamical systems y = Ly for which arbitrarily high order explicit symmetric structure-preserving schemes, i.e. the numerical solutions generated by the schemes satisfy $\det(\frac{\partial y_1}{\partial y_0})=e^{htrL}$, where trL is the trace of matrix L,can be constructed.For nonlinear dynamical systems $\dot{y}=f(y)$ Feng-Shang first-order volume-preserving scheme can be also constructed starting from modified $\theta-$methods and is shown that the scheme is structure-preserving to phase space volume.
Geng Sun. (1970). Structure-Preserving Algorithms for Dynamical Systems. Journal of Computational Mathematics. 20 (6). 619-626. doi:
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