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Almost Symplectic Runge-Kutta Schemes for Hamiltonian Systems

dc.contributor.authorTan, Xiaoboen_US
dc.description.abstractSymplectic Runge-Kutta schemes for the integration of general Hamiltonian systems are implicit. In practice one has to solve the implicit algebraic equations using some iterative approximation method, in which case the resulting integration scheme is no longer symplectic. In this paper we first analyze the preservation of the symplectic structure under two popular approximation schemes, fixed-point iteration and Newton's method, respectively. Error bounds for the symplectic structure are established when N fixed-point iterations or N iterations of Newton's method are used. The implications of these results for the implementation of symplectic methods are discussed and then explored through extensive numerical examples. Numerical comparisons with non-symplectic Runge-Kutta methods and pseudo-symplectic methods are also presented.en_US
dc.format.extent1335292 bytes
dc.relation.ispartofseriesISR; TR 2004-1en_US
dc.relation.ispartofseriesCDCSS; TR 2004-1en_US
dc.subjectSensor-Actuator Networksen_US
dc.titleAlmost Symplectic Runge-Kutta Schemes for Hamiltonian Systemsen_US
dc.typeTechnical Reporten_US

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