作者: 路標(biāo) 時間: 2025-3-22 00:19
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 Nystr?m methods, which can be applied t作者: Comprise 時間: 2025-3-22 02:43
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作者: fatuity 時間: 2025-3-22 07:26 作者: 使激動 時間: 2025-3-22 12:49
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作者: Introvert 時間: 2025-3-22 13:03
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作者: Introvert 時間: 2025-3-22 19:52 作者: athlete’s-foot 時間: 2025-3-23 01:06
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.作者: CAND 時間: 2025-3-23 01:42 作者: Consensus 時間: 2025-3-23 09:23
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作者: 清澈 時間: 2025-3-23 10:13 作者: Ejaculate 時間: 2025-3-23 16:58
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作者: notification 時間: 2025-3-23 20:03
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.作者: Enliven 時間: 2025-3-23 23:15 作者: cloture 時間: 2025-3-24 03:54 作者: 迅速成長 時間: 2025-3-24 08:07
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.作者: Dri727 時間: 2025-3-24 11:53 作者: Hirsutism 時間: 2025-3-24 18:35 作者: 推崇 時間: 2025-3-24 22:17
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.作者: 宏偉 時間: 2025-3-25 01:18
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.作者: 混沌 時間: 2025-3-25 03:43
https://doi.org/10.1007/978-3-662-05018-7Hamiltonian and reversible systems; Numerical integration; calculus; differential equation; differential作者: MITE 時間: 2025-3-25 10:37 作者: Cardiac-Output 時間: 2025-3-25 15:32 作者: 支柱 時間: 2025-3-25 17:03 作者: 轉(zhuǎn)折點 時間: 2025-3-25 21:41
Andreas Patyk,Guido A. Reinhardtsses 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 Nystr?m methods, which can be applied t作者: Panacea 時間: 2025-3-26 02:47 作者: 利用 時間: 2025-3-26 07:51
Die übrigen Kleearten bzw. Futterleguminosenn 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作者: abduction 時間: 2025-3-26 12:08
F. Bazzoli,R. B?hmer,H. J. Weiss. 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作者: 官僚統(tǒng)治 時間: 2025-3-26 14:52 作者: Frisky 時間: 2025-3-26 17:03 作者: ethnology 時間: 2025-3-26 20:57 作者: 大酒杯 時間: 2025-3-27 05:10 作者: angiography 時間: 2025-3-27 07:43
https://doi.org/10.1007/978-94-011-9038-1tic 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作者: 小母馬 時間: 2025-3-27 10:41 作者: 整體 時間: 2025-3-27 17:41
Elektrische und optische Konstanten,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作者: 莊嚴(yán) 時間: 2025-3-27 21:08
Ernst Hairer,Gerhard Wanner,Christian LubichA unique feature of the book is the numerical treatment of KAM theory.There is no other book which deals with this.Includes supplementary material: 作者: 弓箭 時間: 2025-3-28 01:44 作者: 使饑餓 時間: 2025-3-28 03:12 作者: APO 時間: 2025-3-28 07:10 作者: detach 時間: 2025-3-28 11:13
Book 20021st editioncillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The作者: 侵略者 時間: 2025-3-28 17:35
Die übrigen Kleearten bzw. Futterleguminosenthem. In particular, we study projection methods and methods based on local coordinates of the manifold defined by the invariants. We discuss in some detail the case where the manifold is a Lie group.作者: 使高興 時間: 2025-3-28 20:09
Curt F. Kollbrunner,Nikola Hajdinion, which is a formal series in powers of the step size, has to be truncated. The error, induced by such a truncation, can be made exponentially small, and the results remain valid on exponentially long time intervals.作者: 600 時間: 2025-3-29 01:54 作者: monogamy 時間: 2025-3-29 06:36 作者: 食草 時間: 2025-3-29 07:22
Examples and Numerical Experiments,ffects (on a different scale) occur with more sophisticated higher-order integration schemes. The experiments presented here should serve as a motivation for the theoretical and practical investigations of later chapters. The reader is encouraged to repeat the experiments or to invent similar ones.作者: endarterectomy 時間: 2025-3-29 11:28 作者: 突變 時間: 2025-3-29 18:32
Order Conditions, Trees and B-Series,recently found interesting applications in quantum field theory. The chapter terminates with the Baker-CampbellHausdorff formula, which allows another access to the order properties of composition and splitting methods.作者: 無能的人 時間: 2025-3-29 22:12
Symmetric Integration and Reversibility,Runge-Kutta and composition methods, and we show how standard approaches for solving differential equations on manifolds can be symmetrized. A theoretical explanation of the excellent longtime behaviour of symmetric methods applied to reversible differential equations will be given in Chap. XI.
