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# STRUCTURE-PRESERVING ALGORITHMS FOR DYNAMICAL SYSTEMS

Geng Sun
Journal of Computational Mathematics
Vol. 20, No. 6 (NOVEMBER 2002), pp. 619-626
Stable URL: http://www.jstor.org/stable/43693029
Page Count: 8
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## Abstract

We study structure-preserving algorithms to phase space volume for linear dynamical systems ẏ = Ly for which arbitrarily high order explicit symmetric structure-preserving schemes, i.e. the numerical solutions generated by the schemes satisfy $\det \left( {\frac{{{\partial _{y1}}}} {{{\partial _{y0}}}}} \right) = {e^{htrL}}$, where trL is the trace of matrix L, can be constructed. For nonlinear dynamical systems ẏ = f(y) Feng-Shang first-order volume-preserving scheme can be also constructed starting from modified θ - methods and is shown that the scheme is structure-preserving to phase space volume.

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