《Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations》是2018年科學出版社出版的圖書，作者是Xinyuan Wu·Bin Wang。
基本介紹
- 中文名：Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations
- 作者：Xinyuan Wu·Bin Wang
- 出版時間：2018年1月
- 出版社：科學出版社
- ISBN：9787030551283
內容簡介,圖書目錄,
內容簡介
An important area of numerical analysis and scientific computing is geometric numerical integration which is concerned with the discretization of differential equations while respecting their structural invariants and geometry. In the last few decades, numerical simulation for nonlinear oscillators has received a great deal of attention, and many researchers have been concemed with the design and analysis of numerical schemes for solving oscillatory problems. It has been a common practice that a numerical scheme should be designed to preserve as much as pos- sible the (physical/geometric) intrinsic properties of the original continuous sys- tems. Although great advances have by now been made in numerical treatments for oscillatory differential equations, further exploration of novel structure-preserving algorithms is still an active area of research. The objective of this sequel to our previous monograph, which was entitled “Structure-Preserving Algorithms for Oscillatory Diferential Equations I'', is to study further structure-preserving schemes for oscillatory systems that can be modelled by systems of ondinary and partial differential equations. Problems of this type arise in a variety of fields in science and engineering such as quantum physics, celestial mechanics and molecular dynamics.
圖書目錄
1 Functionally Fitted Continuous Finite Element Methods for Oscillatory Hamiltonian Systems
2 Exponential Average-Vector-Field Integrator for Conservative or Dissipative Systems
3 Exponential Fourier Collocation Methods for First-Order Differential Equations
4 Symplectic Exponential Runge-Kutta Methods for Solving Nonlinear Hamiltonian Systems
5 High-Order Symplectic and Symmetric Composition Integrators for Multi-frequency Oscillatory Hamiltonian Systems
6 The Construction of Arbitrary Order ERKN Integrators via Group Theory
7 Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems
8 Compact Tri-Colored Tree Theory for General ERKN Methods
9 An Integral Formula Adapted to Different Boundary Conditions for Arbitrarily High-Dimensional Nonlinear Klein-Gordon Equations
10 An Energy-Preserving and Symmetric Scheme for Nonlinear Hamiltonian Wave Equations
11 Arbitrarily High-Order Time-Stepping Schemes for Nonlinear Klein-Gordon Equations
12 An Essential Extension of the Finite-Energy Condition for ERKN Integrators Solving Nonlinear Wave Equations
Index
