On the Error Reduction of a Simple Symplectic Integrator

Ito Takashi; Tanikawa Kiyotaka

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On the Error Reduction of a Simple Symplectic Integrator

机译：关于简单辛积分器的误差减小

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Ananalysisoftruncationerrorsofthesimplestsymplecticintegratorisrevisited.Weperformedananalyticalerrorestimateofthisintegratorwithintheframeworkofacanonicalperturbationmethod,takingthetwo-bodysystemasanexample.Ourstudywasmotivatedbythedesiretoremoveanyconfusioninthederivationofthisissueinonestandardliteraturealongthislineofresearch.Werepeatedthederivation,andexaminedhowasecularnumericalerrorarisesinsymplecticintegration.Weshowedthatitispossibletosubstantiallyeliminateasecularnumericalerrorbychoosingappropriateinitialconditions,aspreviousstudieshaveshown.Ontheotherhand,dependingonboundaryparametervalues,suchastheeccentricityinthetwo-bodysystem,wecouldseethatitissometimesimpossibletoreducethesecularnumericalerrorbychangingthestartingconditions.Wealsonumericallydemonstratedthisreduction,orlackofreductionofnumericalerrorsbytakingarestrictedthree-bodysystemasanexample.Weconfirmedthattheso-calleda€?iterativestarta€?ofsymplecticintegratorsworksincertainsystems.

机译：Ananalysisoftruncationerrorsofthesimplestsymplecticintegratorisrevisited.Weperformedananalyticalerrorestimateofthisintegratorwithintheframeworkofacanonicalperturbationmethod，takingthetwo bodysystemasanexample.Ourstudywasmotivatedbythedesiretoremoveanyconfusioninthederivationofthisissueinonestandardliteraturealongthislineofresearch.Werepeatedthederivation，andexaminedhowasecularnumericalerrorarisesinsymplecticintegration.Weshowedthatitispossibletosubstantiallyeliminateasecularnumericalerrorbychoosingappropriateinitialconditions，aspreviousstudieshaveshown.Ontheotherhand，dependingonboundaryparametervalues，suchastheeccentricityinthetwo bodysystem，wecouldseethatitissometimesimpossibletoreducethesecularnumericalerrorbychangingthestartingconditions.Wealsonumericallydemonstratedthisreduction，orlackofreductionofnumericalerrorsbytakingarestrictedthree bodysystemasanexample.Weconfirmedthattheso所谓€？Iterativestarta€？Ofsymplecticintegratorsworksincertainsystems。

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《PASJ: Publications of the Astronomical Society of Japan》 |2012年第2期|共页
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Ito Takashi; Tanikawa Kiyotaka;
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1. On the error reduction of a simple symplectic integrator [J] . Ito T., Tanikawa K. PASJ: Publications of the Astronomical Society of Japan . 2012,第2期

机译：关于一个简单辛积分器的误差减小
2. Reduction of Round-off Error in Symplectic Integrators [J] . Toshio Fukushima1 The Astrophysical journal . 2007,第3期

机译：减少辛积分器的舍入误差
3. Exact evolution of time-reversible symplectic integrators and their phase errors for the harmonic oscillator [J] . Chin SA, Scuro SR Physics Letters, A . 2005,第5a6期

机译：时间可逆辛格积分器的精确演化及其相位误差
4. An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 2: Symplecticity and Global Error Analysis [C] . Sadegh Rahrovani, Thomas Abrahamsson, Klas Modin IMAC Conference on Structural Dynamics . 2014

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5. Symplectic integration of simple collisions: A backward error analysis. [D] . Cottrell, David. 2004

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6. Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics [O] . Frédéric Barbaresco, François Gay-Balmaz 2020

机译：Lie Group Coomometom和（多种）杂项集成商：基于Souriau几何统计力学的Lie Group Machine学习新的几何工具
7. On the Error Reduction of a Simple Symplectic Integrator [O] . Takashi Ito, Kiyotaka Tanikawa 2012

机译：关于简单辛集成商的误差减少
8. Simple Method to Generate Integrable Symplectic Maps [R] . Ragnisco, O. 1991

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On the Error Reduction of a Simple Symplectic Integrator

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