Thesubjectofthisbookisgeometricintegratorsfordifferentialequationswithhighlyoscillatorysolutions,includingoscillation-preservingintegrators,continuous-stageERKNintegrators,nonlinearstabilityandconvergenceanalysisofERKNintegrators,functionally-fittedenergy-preservingintegrators,exponentialcollocationmethods,volume-preservingexponentialintegrators,globalerrorboundsofone-stageERKNintegratorsforsemilinearwaveequations,linearly-fittedconservative/dissipativeintegrators,energy-preservingschemesforKlein–Gordonequations,Hermite–BirkhofftimeintegratorsforKlein–Gordonequations,symplecticapproximationsforKlein–Gordonequations,continuous-stagemodifiedleap-frogschemeforhigh-dimensionalHamiltonianwaveequations,semi-analyticalexponentialRKNintegrators,long-timemomentumandactionsbehaviourofenergy-preservingmethods.Thenewgeometricintegratorsareappliedtoproblemswithhighlyoscillatorysolutionsfromsciencesandengineering.

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