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

Geng Sun

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 $\dot{y} = Ly$ 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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COPYRIGHT: © Global Science Press

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@Article{JCM-20-619, author = {Geng Sun}, 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 $\dot{y} = Ly$ 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 AU - Geng Sun 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, phase space volume, source-free dynamical system. AB -

We study structure-preserving algorithms to phase space volume for linear dynamical systems $\dot{y} = Ly$ 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. (2002). Structure-Preserving Algorithms for Dynamical Systems. Journal of Computational Mathematics. 20 (6). 619-626. doi:
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