Line Integral Methods for Conservative Problems

ISBN: 9780367377304 出版年：2016 页码：239 Brugnano, Luigi Iavernaro, Felice CRC Press

A Primer on Line Integral Methods A general framework Geometric integrators Hamiltonian problems Symplectic methods s-stage trapezoidal methods Runge-Kutta line integral methods Examples of Hamiltonian Problems Nonlinear pendulum Cassini ovals Henon-Heiles problem N-body problem Kepler problem Circular restricted three-body problem Fermi-Pasta-Ulam problem Molecular dynamics Analysis of Hamiltonian Boundary Value Methods (HBVMs) Derivation and analysis of the methods Runge-Kutta formulation Properties of HBVMs Least square approximation and Fourier expansion Related approaches Implementing the Methods and Numerical Illustrations Fixed-point iterations Newton-like iterations Recovering round-off and iteration errors Numerical illustrations Hamiltonian Partial Differential Equations The semilinear wave equation Periodic boundary conditions Nonperiodic boundary conditions Numerical tests The nonlinear Schrodinger equation Extensions Conserving multiple invariants General conservative problems EQUIP methods Hamiltonian boundary value problems Appendix: Auxiliary Material Bibliography Index