Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

Establishes structure-preserving algorithms for differential equations Presents theoretical derivations and mathematical analysis Provides high-performance numerical simulations

Autorentext

Xinyuan Wu, a Professor in Department of Mathematics, Nanjing University. His research interests focus on geometric algorithms for differential equations, numerical methods for stiff problems and numerical methods for algebraic systems. In 2017, Wu was awarded with the highest distinction of "Honorary Fellowship" from European Society of Computational Methods in Science and Engineering for the outstanding contribution in the fields of Numerical Analysis and Applied Mathematics. Wu attended the school of Mathematics at the University of Tübingen for study and research from Janurary 19th 2002 to Janurary 20th 2003.

Bin Wang, a Professor in Department of Mathematics and Statistics, Xi'an Jiaotong University. His research interests focus on various structure-preserving algorithms as well as numerical methods for differential equation, especially the numerical computation and analysis of Hamilton ordinary differential equation and partial differential equation. Wang was awarded by Alexander von Humboldt Foundation (2017-2019).

Inhalt
1 Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs.- 2 Continuous-Stage ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions.- 3 Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions.- 4 Functionally-Fitted Energy-Preserving Integrators for Poisson Systems.- 5 Exponential Collocation Methods for Conservative or Dissipative Systems.- 6 Volume-Preserving Exponential Integrators.- 7 Global Error Bounds of One-Stage Explicit ERKN Integrators for Semilinear Wave Equations.- 8 Linearly-Fitted Conservative (Dissipative) Schemes for Nonlinear Wave Equations.- 9 Energy-Preserving Schemes for High-Dimensional Nonlinear KG Equations.- 10 High-Order Symmetric HermiteBirkhoff Time Integrators for Semilinear KG Equations.- 11 Symplectic Approximations for Efficiently Solving Semilinear KG Equations.- 12 Continuous-Stage Leap-Frog Schemes for Semilinear Hamiltonian Wave Equations.- 13 Semi-Analytical ERKN Integrators for Solving High-Dimensional Nonlinear Wave Equations.- 14 Long-Time Momentum and Actions Behaviour of Energy-Preserving Methods for Wave Equations.