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Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

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Cover of 'Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations'

Table of Contents

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    Book Overview
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    Chapter 1 Functionally Fitted Continuous Finite Element Methods for Oscillatory Hamiltonian Systems
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    Chapter 2 Exponential Average-Vector-Field Integrator for Conservative or Dissipative Systems
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    Chapter 3 Exponential Fourier Collocation Methods for First-Order Differential Equations
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    Chapter 4 Symplectic Exponential Runge–Kutta Methods for Solving Nonlinear Hamiltonian Systems
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    Chapter 5 High-Order Symplectic and Symmetric Composition Integrators for Multi-frequency Oscillatory Hamiltonian Systems
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    Chapter 6 The Construction of Arbitrary Order ERKN Integrators via Group Theory
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    Chapter 7 Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems
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    Chapter 8 A Compact Tri-Colored Tree Theory for General ERKN Methods
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    Chapter 9 An Integral Formula Adapted to Different Boundary Conditions for Arbitrarily High-Dimensional Nonlinear Klein–Gordon Equations
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    Chapter 10 An Energy-Preserving and Symmetric Scheme for Nonlinear Hamiltonian Wave Equations
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    Chapter 11 Arbitrarily High-Order Time-Stepping Schemes for Nonlinear Klein–Gordon Equations
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    Chapter 12 An Essential Extension of the Finite-Energy Condition for ERKN Integrators Solving Nonlinear Wave Equations
Attention for Chapter 4: Symplectic Exponential Runge–Kutta Methods for Solving Nonlinear Hamiltonian Systems
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