点击选择搜索分类
首页 - 婚恋与两性- 正文
☆☆☆☆☆
||
[美] Uri,M.Ascher,Linda,R.Petzold 著
出版社: 科学出版社 ISBN:9787030234865 版次:1 商品编码:11918501 包装:精装 丛书名: 国外数学名著系列(续一)(影印版)41 外文名称:Computer Methods for Ordinary Differential Equations and Differential-algebraic Equations 开本:1
List of Tables
Preface
Part Ⅰ:Introduction
1 Ordinary Differential Equations
1.1 IVPs
1.2 BVPs
1.3 Differential-Algebraic Equations
1.4 Families of Application Problems
1.5 Dynamical Systems
1.6 Notation
Part Ⅱ:Initial Value Problems
2 On Problem Stability
2.1 Test Equation and General Definitions
2.2 Linear,Constant-Coefficient Systems
2.3 Linear,Variable-Coefficient Systems
2.4 Nonlinear Problems
2.5 Hamiltonian Systems
2.6 Notes and References
2.7 Exercises
3 Basic Methods,Basic Concepts
3.1 A Simple Method:Forward Euler
3.2 Convergence,Accuracy,Consistency,and O-Stability
3.3 Absolute Stability
3.4 Stiffness:Backward Euler
3.4.1 Backward Euler
3.4.2 Solving Nonlinear Equations
3.5 A-Stability,Stiff Decay
3.6 Symmetry:Trapezoidal Method
3.7 Rough Problems
3.8 Software,Notes,and References
3.8.1 Notes
3.8.2 Software
3.9 Exercises
4 One-Step Methods
4.1 The First Runge-Kutta Methods
4.2 General Formulation of Runge-Kutta Methods
4.3 Convergence,O-Stability,and Order for Runge-Kutta Methods
4.4 Regions of Absolute Stability for Explicit Runge-Kutta Methods
4.5 Error Estimation and Control
4.6 Sensitivity to Data Perturbations
4.7 Implicit Runge-Kutta and Collocation Methods
4.7.1 Implicit Runge-Kutta Methods Based on Collocation
4.7.2 Implementation and Diagonally Implicit Methods...
4.7.3 Order Reduction
4.7.4 More on Implementation and Singly Implicit RungeKutta Methods
4.8 Software,Notes,and References
4.8.1 Notes
4.8.2 Software
4.9 Exercises
5 Linear Multistep Methods
5.1 The Most Popular Methods
5.1.1 Adams Methods
5.1.2 BDF
5.1.3 Initial Values for Multistep Methods
5.2 Order,O-Stability,and Convergence
5.2.1 Order
5.2.2 Stability:Difference Equations and the Root Condition
5.2.3 O-Stability and Convergence
5.3 Absolute Stability
5.4 Implementation of hnplicit Linear Multistep Methods
5.4.1 Functional Iteration
5.4.2 Predictor-Corrector Methods
5.4.3 Modified Newton Iteration
5.5 Designing Multistep General-Purpose Software
5.5.1 Variable Step-Size Formulae
5.5.2 Estimating and Controlling the Local Error
5.5.3 Approximating the Solution at Off-Step Points
5.6 Software,Notes,and References
5.6.1 Notes
5.6.2 Software
5.7 Exercises
Part Ⅲ:Boundary Value Problems
6 More Boundary Value Problem Theory and Applications
6.1 Linear BVPs and Green's Function '.
6.2 Stability of BVPs
6.3 BVP Stiffness
6.4 Some Reformulation Tricks
6.5 Notes and References
6.6 Exercises
7 Shooting
7.1 Shooting:A Simple Method and Its Limitations
7.1.1 Difficulties
7.2 Multiple Shooting
7.3 Software,Notes,and References
7.3.1 Notes
7.3.2 Software
7.4 Exercises
8 Finite Difference Methods for Boundary Value Problems
8.1 Midpoint and Trapezoidal Methods
8.1.1 Solving Nonlinear Problems:Quasi-Linearization
8.1.2 Consistency,O-Stability,and Convergence
8.2 Solving the Linear Equations
8.3 Higher-Order Methods
8.3.1 Collocation
8.3.2 Acceleration Techniques
8.4 More on Solving Nonlinear Problems
8.4.1 Damped Newton
8.4.2 Shooting for Initial Guesses
8.4.3 Continuation
8.5 Error Estimation and Mesh Selection
8.6 Very Stiff Problems
8.7 Decoupling
8.8 Software,Notes,and References
8.8.1 Notes
8.8.2 Software
8.9 Exercises
Part Ⅳ:Differential-Algebraic Equations
9 More on Differential-Algebraic Equations
9.1 Index and Mathematical Structure
9.1.1 Special DAE Forms
9.1.2 DAE Stability
9.2 Index Reduction and Stabilization:ODE with Invariant
9.2.1 Reformulation of Higher-Index DAEs
9.2.2 ODEs with Invariants
9.2.3 State Space Formulation
9.3 Modeling with DAEs
9.4 Notes and References
9.5 Exercises
10 Numerical Methods for Differential-Algebraic Equations
10.1 Direct Discretization Methods
10.1.1 A Simple Method:Backward Euler
10.1.2 BDF and General Multistep Methods
10.1.3 Radau Collocation and Implicit Runge-Kutta Methods
10.1.4 Practical Difficulties
10.1.5 Specialized Runge-Kutta Methods for Hessenberg Index-2 DAEs
10.2 Methods for ODEs on Manifolds
10.2.1 Stabilization of the Discrete Dynamical System
10.2.2 Choosing the Stabilization Matrix F
10.3 Software,Notes,and References
10.3.1 Notes
10.3.2 Software
10.4 Exercises
Bibliography
Index
国外数学名著系列(影印版)41:常微分方程和微分代数方程的计算机方法 [Computer Methods for Ordinary Differential Equations and Differe 电子书 下载 mobi epub pdf txt
国外数学名著系列(影印版)41:常微分方程和微分代数方程的计算机方法 [Computer Methods for Ordinary Differential Equations and Differe-so88
国外数学名著系列(影印版)41:常微分方程和微分代数方程的计算机方法 [Computer Methods for Ordinary Differential Equations and Differe pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[美] Uri,M.Ascher,Linda,R.Petzold 著
出版社: 科学出版社 ISBN:9787030234865 版次:1 商品编码:11918501 包装:精装 丛书名: 国外数学名著系列(续一)(影印版)41 外文名称:Computer Methods for Ordinary Differential Equations and Differential-algebraic Equations 开本:1
内容简介
Designed for those people who want to gain a practical knowledge of modem techniques,this book contains all the material necessary for a course on the nmnerical solution of differential equations.Written by two of the field's leading athorities,it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential- algebraic equations.The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition.It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well informed introduction that emphasizes basic methods and theory,issues in the use and development of mathematical software,and examples from scientific engineering applications.Topics requiring an extensive amount of mathematical development,such as symplectic methods for Hamiltonian systems,are introduced,motivated,and included in the exercises,but a complete and rigorous mathematical presentation is referenced rather than included. This book is appropriate for senior undergraduate or beginning graduate students with a computational focus and practicing engineers and scientists who want to learn about computational differential equations.A beginning course in numerical analysis is needed,and a beginning course in ordinary differential equations would be helpful.内页插图
目录
List of FiguresList of Tables
Preface
Part Ⅰ:Introduction
1 Ordinary Differential Equations
1.1 IVPs
1.2 BVPs
1.3 Differential-Algebraic Equations
1.4 Families of Application Problems
1.5 Dynamical Systems
1.6 Notation
Part Ⅱ:Initial Value Problems
2 On Problem Stability
2.1 Test Equation and General Definitions
2.2 Linear,Constant-Coefficient Systems
2.3 Linear,Variable-Coefficient Systems
2.4 Nonlinear Problems
2.5 Hamiltonian Systems
2.6 Notes and References
2.7 Exercises
3 Basic Methods,Basic Concepts
3.1 A Simple Method:Forward Euler
3.2 Convergence,Accuracy,Consistency,and O-Stability
3.3 Absolute Stability
3.4 Stiffness:Backward Euler
3.4.1 Backward Euler
3.4.2 Solving Nonlinear Equations
3.5 A-Stability,Stiff Decay
3.6 Symmetry:Trapezoidal Method
3.7 Rough Problems
3.8 Software,Notes,and References
3.8.1 Notes
3.8.2 Software
3.9 Exercises
4 One-Step Methods
4.1 The First Runge-Kutta Methods
4.2 General Formulation of Runge-Kutta Methods
4.3 Convergence,O-Stability,and Order for Runge-Kutta Methods
4.4 Regions of Absolute Stability for Explicit Runge-Kutta Methods
4.5 Error Estimation and Control
4.6 Sensitivity to Data Perturbations
4.7 Implicit Runge-Kutta and Collocation Methods
4.7.1 Implicit Runge-Kutta Methods Based on Collocation
4.7.2 Implementation and Diagonally Implicit Methods...
4.7.3 Order Reduction
4.7.4 More on Implementation and Singly Implicit RungeKutta Methods
4.8 Software,Notes,and References
4.8.1 Notes
4.8.2 Software
4.9 Exercises
5 Linear Multistep Methods
5.1 The Most Popular Methods
5.1.1 Adams Methods
5.1.2 BDF
5.1.3 Initial Values for Multistep Methods
5.2 Order,O-Stability,and Convergence
5.2.1 Order
5.2.2 Stability:Difference Equations and the Root Condition
5.2.3 O-Stability and Convergence
5.3 Absolute Stability
5.4 Implementation of hnplicit Linear Multistep Methods
5.4.1 Functional Iteration
5.4.2 Predictor-Corrector Methods
5.4.3 Modified Newton Iteration
5.5 Designing Multistep General-Purpose Software
5.5.1 Variable Step-Size Formulae
5.5.2 Estimating and Controlling the Local Error
5.5.3 Approximating the Solution at Off-Step Points
5.6 Software,Notes,and References
5.6.1 Notes
5.6.2 Software
5.7 Exercises
Part Ⅲ:Boundary Value Problems
6 More Boundary Value Problem Theory and Applications
6.1 Linear BVPs and Green's Function '.
6.2 Stability of BVPs
6.3 BVP Stiffness
6.4 Some Reformulation Tricks
6.5 Notes and References
6.6 Exercises
7 Shooting
7.1 Shooting:A Simple Method and Its Limitations
7.1.1 Difficulties
7.2 Multiple Shooting
7.3 Software,Notes,and References
7.3.1 Notes
7.3.2 Software
7.4 Exercises
8 Finite Difference Methods for Boundary Value Problems
8.1 Midpoint and Trapezoidal Methods
8.1.1 Solving Nonlinear Problems:Quasi-Linearization
8.1.2 Consistency,O-Stability,and Convergence
8.2 Solving the Linear Equations
8.3 Higher-Order Methods
8.3.1 Collocation
8.3.2 Acceleration Techniques
8.4 More on Solving Nonlinear Problems
8.4.1 Damped Newton
8.4.2 Shooting for Initial Guesses
8.4.3 Continuation
8.5 Error Estimation and Mesh Selection
8.6 Very Stiff Problems
8.7 Decoupling
8.8 Software,Notes,and References
8.8.1 Notes
8.8.2 Software
8.9 Exercises
Part Ⅳ:Differential-Algebraic Equations
9 More on Differential-Algebraic Equations
9.1 Index and Mathematical Structure
9.1.1 Special DAE Forms
9.1.2 DAE Stability
9.2 Index Reduction and Stabilization:ODE with Invariant
9.2.1 Reformulation of Higher-Index DAEs
9.2.2 ODEs with Invariants
9.2.3 State Space Formulation
9.3 Modeling with DAEs
9.4 Notes and References
9.5 Exercises
10 Numerical Methods for Differential-Algebraic Equations
10.1 Direct Discretization Methods
10.1.1 A Simple Method:Backward Euler
10.1.2 BDF and General Multistep Methods
10.1.3 Radau Collocation and Implicit Runge-Kutta Methods
10.1.4 Practical Difficulties
10.1.5 Specialized Runge-Kutta Methods for Hessenberg Index-2 DAEs
10.2 Methods for ODEs on Manifolds
10.2.1 Stabilization of the Discrete Dynamical System
10.2.2 Choosing the Stabilization Matrix F
10.3 Software,Notes,and References
10.3.1 Notes
10.3.2 Software
10.4 Exercises
Bibliography
Index
前言/序言
国外数学名著系列(影印版)41:常微分方程和微分代数方程的计算机方法 [Computer Methods for Ordinary Differential Equations and Differe 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 冰上冰下大探险-海底小纵队梦想剧场
- 手机摄影从入门到精通 视频讲解版 手机摄影教程书籍
- (青少年“海洋梦”系列丛书)北海浩歌——海洋生态与文明 9787565024153
- 清末民初文献丛刊第一辑(套装共34册)
- 深海怪兽跑出来了:超好玩的AR互动4D海洋动物小百科9787508666006【新华书店
- 【WF】 钢笔画手绘表现技法从入门到精通
- 揭秘垃圾-尤斯伯恩看里面
- 中国书法史(套装七卷)先秦秦代 两汉 魏晋南北朝 隋唐五代 宋辽金 元明 清代卷
- (青少年“海洋梦”系列丛书)凌波踏浪——航海设备与舰只
- 碎片光泽 摄影创意与创新之旅(附光盘) 李子青 9787302460602
- 芝麻大问号?-2-芝麻的科学书
- 佳能EOS 5D Mark 3专业解析 英普丽斯摄影 清华大学出版社
- 蔚蓝星汉:奇趣海岛 9787565024191
- 正版现货 荒木经惟的天才写真术(修订版) 荒木经惟 北京联合出版公司
- 让我们运动吧!-听爸爸讲科普-(低幼版)