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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Continuous-Stage ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions,s, sufficient conditions for energy preservation are shown for CSERKN methods. The symmetry and stability of CSERKN integrators are also analysed in detail. Preliminary numerical results highlight the effectiveness of CSERKN methods.

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细胞学

Exponential Collocation Methods for Conservative or Dissipative Systems,ent systems. As a consequence of this discussion, arbitrary-order trigonometric/RKN collocation methods are also presented and analysed for second-order highly oscillatory/general systems. The chapter is accompanied by numerical results that demonstrate the potential value of this research.

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Volume-Preserving Exponential Integrators,onential integrators are demonstrated. For solving highly oscillatory second-order systems, efficient volume-preserving exponential integrators are derived, and for separable partitioned systems, volume-preserving ERKN integrators are presented. Moreover, volume-preserving RKN methods are also investigated.

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