Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations (Paperback, Softcover Repri)

Functionally ?tted continuous ?nite element methods for oscillatory Hamiltonian system.- Exponential average-vector-?eld integrator for conservative or dissipative systems.- Exponential Fourier collocation methods for ?rst-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 ?nite-energy condition for ERKN integrators solving nonlinear wave equations.- Index