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    • 几何数值积分(第2版)(英文版)
      • 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
      • ISBN:9787519219376
      • 出版日期:2017/01/01
      • 页数:672
    • 售价:48
  • 内容大纲

        E.海尔、C.卢比希、G.万纳著的《几何数值积分((第2版)(英文版)》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。
  • 作者介绍

  • 目录

    I.Examples and Numerical Experiments
      I.1 First Problems and Methods
        I.1.1  The Lotka-Volterra Model
        I.1.2  First Numerical Methods
        I.1.3  The Pendulum as a Hamiltonian System
        I.1.4  The St6rmer-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 Problem
        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  Nystr6m 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 Conditions 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.l.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 Partitioned 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 Exponential and Its Inverse
        III.4.2  The BCH Formula

      II1.5  Order Conditions via the BCH Formula
        1II.5.1  Calculus of Lie Derivatives
        III.5.2  Lie Brackets and Commutativity
        III.5.3  Splitting Methods
        II1.5.4  Composition Methods
      III.6  Exercises
    IV.Conservation of First Integrals and Methods on Manifolds
      IV.1  Examples of First Integrals
      IV.2  Quadratic Invariants
        IV.2.1  Runge-Kutta Methods
        IV.2.2  Partitioned Runge-Kutta 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  Projection 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  Differential Equations on Lie Groups
      1V.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
    VI.Symplectic Integration of Hamiltonian Systems
    VII.Non-Canonical Hamiitonian 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.Dissivativeiv Perturbed Hamiltonian and Reversible Systems
    XIII.Oscillatory Differential Equations with Constant High Frequencies
    XIV.Oscillatory Differential Equations with Varying High Frequencies
    XV.Dynamics of Multistep Methods
    Bibliography
    Index

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