Structure-Preserving Algorithms for Oscillatory Differential Equations II [1st ed.] 3662481553, 9783662481554

This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscilla

299 79 3MB

English Pages 298 [305] Year 2015

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Structure-Preserving Algorithms for Oscillatory Differential Equations II [1st ed.]
3662481553, 9783662481554

Author / Uploaded
Xinyuan Wu
Kai Liu
Wei Shi

Table of contents :
Front Matter....Pages i-xv
Matrix-Variation-of-Constants Formula....Pages 1-21
Improved Störmer–Verlet Formulae with Applications....Pages 23-51
Improved Filon-Type Asymptotic Methods for Highly Oscillatory Differential Equations....Pages 53-68
Efficient Energy-Preserving Integrators for Multi-frequency Oscillatory Hamiltonian Systems....Pages 69-93
An Extended Discrete Gradient Formula for Multi-frequency Oscillatory Hamiltonian Systems....Pages 95-115
Trigonometric Fourier Collocation Methods for Multi-frequency Oscillatory Systems....Pages 117-148
Error Bounds for Explicit ERKN Integrators for Multi-frequency Oscillatory Systems....Pages 149-174
Error Analysis of Explicit TSERKN Methods for Highly Oscillatory Systems....Pages 175-192
Highly Accurate Explicit Symplectic ERKN Methods for Multi-frequency Oscillatory Hamiltonian Systems....Pages 193-209
Multidimensional ARKN Methods for General Multi-frequency Oscillatory Second-Order IVPs....Pages 211-227
A Simplified Nyström-Tree Theory for ERKN Integrators Solving Oscillatory Systems....Pages 229-253
General Local Energy-Preserving Integrators for Multi-symplectic Hamiltonian PDEs....Pages 255-291
Back Matter....Pages 293-298

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