网站首页 软件下载 游戏下载 翻译软件 电子书下载 电影下载 电视剧下载 教程攻略 音乐专区
霍普软件下载网电子书栏目提供海量电子书在线免费阅读及下载。
| 电子书 | 几何数值积分(第2版)(英文版) |
| 分类 | 电子书下载 |
| 作者 | (瑞士)E.海尔//C.卢比希//G.万纳 |
| 出版社 | 世界图书出版公司 |
| 下载 |
|
| 介绍 |
内容推荐 《几何数值积分》是一部教科书，旨在向大学3-4年级学生介绍哈密顿系统，可逆系统流型上的微分方程和高频振荡解问题。书中全面论述了辛理论和对称法。第2版主要增加了非典型哈密顿系统，高频振荡机械系统和多步法动力学。本书各章有习题。读者对象：数学等相关专业的大学高年级本科书和低年研究生。 目录 Ⅰ.Examples and Numerical Experiments
Ⅰ.1 First Problems and Methods Ⅰ.1.1 The Lotka—Vokerra Model Ⅰ.1.2 First Numerical Methods Ⅰ.1.3 The Pendulum as a Hamiltonian System. Ⅰ.1.4 The Stormer—Verlet Scheme Ⅰ.2 The Kepler Problem and the Outer Solar System Ⅰ.2.1 Angular Momentum and Kepler's Second Law Ⅰ.2.2 Exact Integration of the Kepler Problem Ⅰ.2.3 Numerical Integration of the Kepler Problem Ⅰ.2.4 The Outer Solar System Ⅰ.3 The Henon—Heiles Model Ⅰ.4 Molecular Dynamics Ⅰ.5 Highly Oscillatory Problems Ⅰ.5.1 A Fermi—Pasta—Ulam Ptoblem Ⅰ.5.2 Application of Classical Integrators Ⅰ.6 Exercises Ⅱ.Numerical Integrators Ⅱ.1 Runge—Kutta and Collocation Methods Ⅱ.1.1 Runge—Kutta Methods Ⅱ.1.2 Collocation Methods Ⅱ.1.3 Gauss and Lobatto Collocation Ⅱ.1.4 Discontinuous Collocation Methods Ⅱ.2 Partitioned Runge—Kutta Methods Ⅱ.2.1 Definition and First Examples Ⅱ.2.2 Lobatto IIIA—IIIB Pairs Ⅱ.2.3 Nystrom Methods Ⅱ.3 The Adjoint of a Method Ⅱ.4 Composition Methods Ⅱ.5 Splitting Methods Ⅱ.6 Exercises Ⅲ.Order Conditions， Trees and B—Series Ⅲ.1 Runge—Kutta Order Condiuons and B—Series Ⅲ.1.1 Derivation of the Order Conditions Ⅲ.1.2 B—Series Ⅲ.1.3 Composition of Methods Ⅲ.1.4 Composition of B—Series Ⅲ.1.5 The Butcher Group Ⅲ.2 Order Conditions for Partitioned Runge—Kutta Methods Ⅲ.2.1 Bi—Coloured Trees and P—Series Ⅲ.2.2 Order Conditions for Panitioned Runge—Kutta Methods Ⅲ.2.3 Order Conditions for Nystrom Methods Ⅲ.3 Order Conditions for Composition Methods Ⅲ.3.1 Introduction Ⅲ.3.2 The General Case Ⅲ.3.3 Reduction of the Order Conditions Ⅲ.3.4 Order Conditions for Splitting Methods Ⅲ.4 The Baker—Campbell—Hausdorff Formula Ⅲ.4.1 Derivative of the Exponcntial and Its Inverse Ⅲ.4.2 The BCH Formula Ⅲ.5 Order Conditions via the BCH Formula Ⅲ.5.1 Calculus of Lie Derivatjves Ⅲ.5.2 Lie Brackets and Commutativity Ⅲ.5.3 Splitting Methods Ⅲ.5.4 Composition Methods Ⅲ.6 Exercises Ⅳ.Conservation of First Integrals and Methods on Manifolds Ⅳ.1 Examples of First Integrals Ⅳ.2 Quadratic Invariams Ⅳ.2.1 Runge—Kutta Methods Ⅳ.2.2 Partieioned Runge—Kmta Methods Ⅳ.2.3 Nystrom Methods Ⅳ.3 Polynomial Invariants Ⅳ.3.1 The Determinant as a First Integral Ⅳ.3.2 Isospectral Flows Ⅳ.4 Projeccion Methods Ⅳ.5 Numerical Methods Based on Local Coordinates Ⅳ.5.1 Manifolds and the Tangent Space Ⅳ.5.2 Differential Equations on Manifolds Ⅳ.5.3 Numerical Integrators on Manifolds Ⅳ.6 Differemial Equations on Lie Groups Ⅳ.7 Methods Based on the Magnus Series Expansion Ⅳ.8 Lie Group Methods Ⅳ.8.1 Crouch—Grossman Methods Ⅳ.8.2 Munthe—Kaas Methods Ⅳ.8.3 Further Coordinate Mappings Ⅳ.9 Geometric Numerical Integration Meets Geometric Numerical Linear Algebra Ⅳ.9.1 Numerical Integration on the Stiefel Manifold Ⅳ.9.2 Differential Equations on the Grassmann Manifold Ⅳ.9.3 Dynamical Low—Rank Approximation Ⅳ.10 Exercises Ⅴ.Symmetric Integration and Reversibility Ⅴ.1 Reversible Differential Equations and Maps Ⅴ.2 Symmetric Runge—Kutta Methods Ⅴ.2.1 Collocation and Runge—Kutta Methods Ⅴ.2.2 Partitioned Runge—Kutta Methods Ⅴ.3 Symmetric Composition Methods Ⅴ.3.1 Symmetric Composition of First Order Methods Ⅴ.3.2 Symmetric Composition of Symmetric Methods Ⅴ.3.3 Effective Ordef and Processing Methods Ⅴ.4 Symmetric Methods on Manifolds Ⅴ.4.1 Symmetric Projection Ⅴ.4.2 Symmetric Methods Based on Local Coordinates Ⅴ.5 Energy—Momentum Methods and Discrete Gradients Ⅴ.6 Exercises Ⅵ.Symplectic Integration of Hamiltonian Systems Ⅵ.1 Hamiltonian Systems Ⅵ.1.1 Lagrange's Equations Ⅵ.1.2 Hamilton's Canonical Equations Ⅵ.2 Symplectic Transformations Ⅵ.3 First Examples of Symplectic Integrators Ⅵ.4 Symplectic Runge—Kutta Methods Ⅵ.4.1 Criterion of Symplecticity Ⅵ.4.2 Connection Between Symplecuc and Symmetric Methods Ⅵ.5 Generating Functions Ⅵ.5.1 Existence of Generating Functions Ⅵ.5.2 Generating Function for Symplectic Runge—Kutta Methods Ⅵ.5.3 The Hamilton—Jacobi Partial Differential Equation Ⅵ.5.4 Methods Based on Generating Functions Ⅵ.6 Variational Integrators Ⅵ.6.1 Hamilton's Principle Ⅵ.6.2 Discretization of Hamilton's Principle Ⅵ.6.3 Symplectic Panitioned Runge—Kutta Methods Revisited Ⅵ.6.4 Noether's Theorem Ⅵ.7 Characterization of Symplecuc Methods Ⅵ.7.1 B—Series Methods Conserving Quadratic First Integrals Ⅵ.7.2 Characterization of Symplectic P—Series （and B—Series） Ⅵ.7.3 Ineducible Runge—Kutta Methods Ⅵ.7.4 Characterization oflfreducible Symplectic Methods Ⅵ.8 Conjugate Symplecticity Ⅵ.8.1 Examples and Order Conditions Ⅵ.8.2 Near Conservation of Quadratic First Integrals Ⅵ.9 Volume Preservation Ⅵ.10 Exercises …… Ⅶ.Non—Canonical Hamiltonian Systems Ⅷ.Structure.Preserving Implementation Ⅸ.Backward Error Analysis and Structure Preservation Ⅹ.Hamiltonian Perturbation Theory and Symplectic Integrators Ⅺ.Reversible Perturbation Theory and Symmetric Integrators Ⅻ.Dissipatively Perturbed Hamikonian and Reversible Systems ⅩⅢ.Oscillatory Differential Equations with Constant High Frequencies ⅩⅣ.Oscillatory Differential Equahons with Varying High Frequencies ⅩⅤ.Dynanucs of Multistep Methods Bibliography Index |
| 截图 | |
| 随便看 |
|
免责声明
本网站所展示的内容均来源于互联网，本站自身不存储、不制作、不上传任何内容，仅对网络上已公开的信息进行整理与展示。
本站不对所转载内容的真实性、完整性和合法性负责，所有内容仅供学习与参考使用。
若您认为本站展示的内容可能存在侵权或违规情形，请您提供相关权属证明与联系方式，我们将在收到有效通知后第一时间予以删除或屏蔽。
本网站对因使用或依赖本站信息所造成的任何直接或间接损失概不承担责任。联系邮箱：101bt@pm.me