Structure-Preserving Algorithms for Oscillatory Differential Equations II

by Xinyuan Wu

Matrix-variation-of-constants formula.- Improved St ¨ormer-Verlet formulae with applications.- Improved Filon-type asymptotic methods for highly oscillatory differential equations.- Efficient energy-preserving integrators for multi-frequency oscillatory Hamiltonian systems.- An extended discrete gradient formula for multi-frequency oscillatory Hamiltonian systems.- Trigonometric Fourier collocation methods for multi-frequency oscillatory systems.- Error bounds for explicit ERKN integrators for multi-frequency oscillatory systems.- Error analysis of explicit TSERKN methods for highly oscillatory systems.- Highly accurate explicit symplectic ERKN methods for multi-frequency oscillatory Hamiltonian systems.- Multidimensional ARKN methods for general multi-frequency oscillatory second-order IVPs.- A simplified Nystr¨om-tree theory for ERKN integrators solving oscillatory systems.- An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations.

316 pages, Paperback

Published March 5, 2016