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

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书目名称Geometric Numerical Integration影响因子(影响力)




书目名称Geometric Numerical Integration影响因子(影响力)学科排名




书目名称Geometric Numerical Integration网络公开度




书目名称Geometric Numerical Integration网络公开度学科排名




书目名称Geometric Numerical Integration被引频次




书目名称Geometric Numerical Integration被引频次学科排名




书目名称Geometric Numerical Integration年度引用




书目名称Geometric Numerical Integration年度引用学科排名




书目名称Geometric Numerical Integration读者反馈




书目名称Geometric Numerical Integration读者反馈学科排名

路标

Numerical Integrators,sses of numerical methods. We start with Runge-Kutta and collocation methods, and we introduce discontinuous collocation methods, which cover essentially all high-order implicit Runge-Kutta methods of interest. We then treat partitioned Runge-Kutta methods and Nyström methods, which can be applied t

Comprise

Order Conditions, Trees and B-Series,ed Runge-Kutta methods, and composition methods by using the notion of rooted trees and B-series. These ideas lead to algebraic structures which have recently found interesting applications in quantum field theory. The chapter terminates with the Baker-CampbellHausdorff formula, which allows another

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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

Introvert

Symplectic Integration of Hamiltonian Systems,ng property of these systems is the symplecticity of the flow. As indicated in the following diagram, . Hamiltonian theory operates in three different domains (equations of motion, partial differential equations and variational principles) which are all interconnected. Each of these viewpoints, whic

Introvert

athlete’s-foot

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.

CAND

Consensus

Reversible Perturbation Theory and Symmetric Integrators,tic methods applied to (near-)integrable Hamiltonian systems: linear error growth, long-time near-conservation of first integrals, existence of invariant tori. The present chapter gives a theoretical explanation of the good long-time behaviour of symmetric methods. The results and techniques are lar