Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

• Main Authors: Wu, Xinyuan (Author, http://id.loc.gov/vocabulary/relators/aut), Wang, Bin (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Subjects: Algorithms.; Computational complexity.; Mathematics of Algorithmic Complexity.; Complexity.

The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically...

Table of Contents:

• Functionally fitted continuous finite element methods for oscillatory Hamiltonian system
• Exponential average-vector-field integrator for conservative or dissipative systems
• Exponential Fourier collocation methods for first-order differential Equations
• Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
• High-order symplectic and symmetric composition integrators for multi-frequency oscillatory Hamiltonian systems
• The construction of arbitrary order ERKN integrators via group theory
• Trigonometric collocation methods for multi-frequency and multidimensional oscillatory systems
• A compact tri-colored tree theory for general ERKN methods
• An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations
• An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations
• Arbitrarily high-order time-stepping schemes for nonlinear Klein-Gordon equations
• An essential extension of the finite-energy condition for ERKN integrators solving nonlinear wave equations
• Index.