Scientific Computing with Ordinary Differential Equations用常微分方程作科学计算
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作者： Peter Deuflhard 著
出 版 社：
出版时间： 2002-9-1字数：版次： 1页数： 485印刷时间： 2002/09/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387954622包装： 精装内容简介
This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. The book strictly presents numerical analysis as part of the more general field of scientific computing. Important algorithmic concepts are explained down to questions of software implementation. For initial value problems a dynamical systems approach is used to develop Runge-Kutta, extrapolation, and multistep methods. For boundary value problems including optimal control problems both multiple shooting and collocation methods are worked out in detail. Graduate students and researchers in mathematics, computer science, and engineering will find this book useful. Chapter summaries, detailed illustrations, and exercises are contained throughout the book with many interesting applications taken from a rich variety of areas.Peter Deuflhard is founder and president of the Zuse Institute Berlin (ZIB) and full professor of scientific computing at the Free University of Berlin, department of mathematics and computer science.Folkmar Bornemann is full professor of scientific computing at the Center of Mathematical Sciences, Technical University of Munich.
目录
Preface
Outline
1Time-Dependent Processes in Science and Engineering
1.1 Newton's Celestial Mechanics
1.2 Classical Molecular Dynamics
1.3 Chemical Reaction Kinetics
1.4 Electrical Circuits
Exercises
2 Existence and Uniqueness for Initial Value Problems
2.1 Global Existence and Uniqueness
2.2 Examples of Maximal Continuation
2.3 Structure of Nonunique Solutions
2.4 Weakly Singular Initial Value Problems
2.5 Singular Perturbation Problems
2.6 Quasilinear Differential-Algebraic Problems
Exercises
3 Condition of Initial Value Problems
3.1 Sensitivity Under Perturbations
3.1.1 Propagation Matrices
3.1.2 Condition Numbers
3.1.3 Perturbation Index of DAE Problems
3.2 Stability of ODEs
3.2.1 Stability Concept
3.2.2 Linear Autonomous ODEs
3.2.3 Stability of Fixed Points
3.3 Stability of Recursive Mappings
3.3.1 Linear Autonomous Recursions
3.3.2 Spectra of Rational Matrix Functions
Exercises
4One-Step Methods for Nonstiff IVPs
4.1 Convergence Theory
4.1.1 Consistency
4.1.2 Convergence
4.1.3 Concept of Stiffness
4.2 Explicit Runge-Kutta Methods
4.2.1 Concept of Runge-Kutta Methods
4.2.2 Classical Runge-Kutta Methods
4.2.3 Higher-Order Runge-Kutta Methods
4.2.4 Discrete Condition Numbers
4.3 Explicit Extrapolation Methods
4.3.1 Concept of Extrapolation Methods
4.3.2 Asymptotic Expansion of Discretization Error
4.3.3 Extrapolation of Explicit Midpoint Rule
4.3.4 Extrapolation of StSrmer/Verlet Discretization
Exercises
5Adaptive Control of One-Step Methods
5.1 Local Accuracy Control
5.2 Control-Theoretic Analysis
5.2.1 Excursion to PID Controllers
5.2.2 Step-size Selection as Controller
5.3 Error Estimation
5.4 Embedded Runge-Kutta Methods
5.5 Local Versus Achieved Accuracy
Exercises
6 One-Step Methods for Stiff ODE and DAE IVPs
6.1 Inheritance of Asymptotic Stability
6.1.1 Rational Approximation of Matrix Exponential
6.1.2 Stability Domains
6.1.3 Stability Concepts
6.1.4 Reversibility and Discrete Isometries
……
7 Multistep Methods for ODE and DAE IVPs
8 Boundary Value Problems for ODEs
References
Software
Index
