Titlebook: Geometric Numerical Integration; Structure-Preserving Ernst Hairer,Gerhard Wanner,Christian Lubich Book 2006Latest edition Springer-Verlag

Hormones

Coordinate

Conservation of First Integrals and Methods on Manifolds,n manifolds. Our investigation will follow two directions. We first investigate which of the methods introduced in Chap. II conserve invariants automatically. We shall see that most of them conserve linear invariants, a few of them quadratic invariants, and none of them conserves cubic or general no

BLANK

Symmetric Integration and Reversibility,s. We discuss reversible differential equations and reversible maps, and we explain how symmetric integrators are related to them. We study symmetric Runge–Kutta and composition methods, and we show how standard approaches for solving differential equations on manifolds can be symmetrized. A theoret

明确

Structure-Preserving Implementation,not deteriorate the correct qualitative behaviour of the solution.We study multiple time stepping strategies, the effect of round-off in long-time integrations, and the efficient solution of nonlinear systems arising in implicit integration schemes.

外貌

Hamiltonian Perturbation Theory and Symplectic Integrators, in what is for the theoretician a rather disappointing way. With modern calculating machines, one is now able to compute directly results even more accurately than those provided by perturbation theory.

Unsaturated-Fat

Debrief

Dissipatively Perturbed Hamiltonian and Reversible Systems,ame is true for symmetric methods applied to non-reversible perturbations of reversible systems. In this chapter we study the behaviour of numerical integrators when they are applied to dissipative perturbations of integrable systems, where only one invariant torus persists under the perturbation an

HAWK

Oscillatory Differential Equations with Constant High Frequencies,new complete function evaluation only after a time step over one or many periods of the fastest oscillations in the system. Various such methods have been proposed in the literature – some of them decades ago, some very recently, motivated by problems from molecular dynamics, astrophysics and nonlin

BROOK

强化