Titlebook: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions; Xinyuan Wu,Bin Wang Book 2021 The Editor(s) (if applic

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A. Karlin,D. A. Cowburn,M. J. ReiterThis chapter presents a class of energy-preserving integrators for Poisson systems based on the functionally-fitted strategy, and these energy-preserving integrators can have arbitrarily high order. This approach permits us to obtain the energy-preserving methods proposed by Cohen and Hairer and Brugnano et al. for Poisson systems.

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Role of Decomposition on Drug Stability,Incorporating the operator-variation-of-constants formula for high-dimensional nonlinear wave equations with Fast Fourier Transform techniques in this chapter, we present a class of semi-analytical ERKN integrators, which can nearly preserve the spatial continuity as well as the oscillations of the underlying nonlinear waves equations.

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Functionally-Fitted Energy-Preserving Integrators for Poisson Systems,This chapter presents a class of energy-preserving integrators for Poisson systems based on the functionally-fitted strategy, and these energy-preserving integrators can have arbitrarily high order. This approach permits us to obtain the energy-preserving methods proposed by Cohen and Hairer and Brugnano et al. for Poisson systems.

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Global Error Bounds of One-Stage Explicit ERKN Integrators for SemilinearWave Equations,In this chapter, we analyse global error bounds for one-stage explicit extended Runge–Kutta–Nyström integrators for semilinear wave equations with periodic boundary conditions. We show optimal second-order convergence without requiring Lipschitz continuity and higher regularity of the exact solution.

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