Titlebook: Geometric Numerical Integration; Structure-Preserving Ernst Hairer,Gerhard Wanner,Christian Lubich Book 20021st edition Springer-Verlag Ber

清澈

Ejaculate

Highly Oscillatory Differential Equations,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 nonlinea

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https://doi.org/10.1007/978-3-0348-6326-1In this chapter we study the long-time behaviour of symplectic integrators, combining backward error analysis and the perturbation theory of integrable Hamiltonian systems.

Enliven

cloture

迅速成長

Dynamics of Multistep Methods,Multistep methods are the basis of important codes for nonstiff differential equations (Adams methods) and for stiff problems (BDF methods). We study here their applicability to long-time integrations of Hamiltonian or reversible systems.

Dri727

Hirsutism

推崇

Further Topics in Structure Preservation,ed in Chap. VI. In particular we study symmetric and symplectic methods for constrained Hamiltonian systems, we present Poisson integrators for Hamiltonian problems with a non-standard structure matrix, and we give volume-preserving algorithms for divergence-free differential equations that are not necessarily Hamiltonian systems.

宏偉

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.