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內容簡介

　　This book shows how to derive，test and analyze numerical methods for solving differential equations，including both ordinary and partial differential equations.The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises，which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations，the book includes a large collection of supplemental material： exercise sets，MATLAB computer codes for both student and instructor，lecture slides and movies.

內頁插圖

目錄

Preface

1 Initial Value Problems
1．1 Introduction
1．1．1 Examples of IVPs
1．2 Methods Obtained from Numerical Differentiation．
1．2．1 The Five Steps
1．2．2 Additional Difference Methods
1．3 Methods Obtained from Numerical Quadrature
1．4 Runge——Kutta Methods
1．5 Extensions and Ghost Points
1．6 Conservative Methods
1．6．1 Velocity Verlet
1．6．2 Symplectic Methods
1．7 Next Steps
Exercises

2 Two-Point Boundary Value Problems
2．1 Introduction
2．1．1 Birds on a Wire
2．1．2 Chemical Kinetics
2．2 Derivative Approximation Methods
2．2．1 Matrix Problem
2．2．2 Tridiagonal Matrices
2．2．3 Matrix Problem Revisited
2．2．4 Error Analysis
2．2．5 Extensions
2．3 Residual Methods
2．3．1 Basis Functions
2．3．2 Residual
2．4 Shooting Methods
2．5 Next Steps
Exercises

3 Diffusion Problems
3．1 Introduction
3．1．1 Heat Equation
3．2 Derivative Approximation Methods
3．2．1 Implicit Method
3．2．2 Theta Method
3．3 Methods Obtained from Numerical Quadrature
3．3．1 Crank-Nicolson Method
3．3．2 L-Stability
3．4 Methods of Lines
3．5 Collocation
3．6 Next Steps
Exercises

4 Advection Equation
4．1 Introduction
4．1．1 Method of Characteristics
4．1．2 Solution Properties
4．1．3 Boundary Conditions
4．2 First-Order Methods
4．2．1 Upwind Scheme
4．2．2 Downwind Scheme
4．2．3 blumericul Domu'm of Dependence
4．2．4 Stability
4．3 Improvements
4．3．1 Lax-Wendroff Method
4．3．2 Monotone Methods
4．3．3 Upwind Revisited
4．4 Implicit Methods
Exercises

5 Numerical Wave Propagation
5．1 Introduction
5．1．1 Solution Methods
5．1．2 Plane Wave Solutions
5．2 Explicit Method
5．2．1 Diagnostics
5．2．2 Numerical Experiments
5．3 Numerical Plane Waves
5．3．1 Numerical Group Velocity
5．4 Next Steps
Exercises

6 Elliptic Problems
6．1 Introduction
6．1．1 Solutions
6．1．2 Properties of the Solution
6．2 Finite Difference Approximation
6．2．1 Building the Matrix
6．2．2 Positive Definite Matrices
6．3 Descent Methods
6．3．1 Steepest Descent Method
6．3．2 Conjugate Gradient Method
6．4 Numerical Solution of Laplace's Equation
6．5 Preconditioned Conjugate Gradient Method
6．6 Next Steps
Exercises

A Appendix
A．1 Order Symbols
A．2 Taylor's Theorem
A．3 Round-Off Error
A．3．1 Fhnction Evaluation
A．3．2 Numerical Differentiation
A．4 Floating-Point Numbers

References

Index

前言/序言

國外數學名著係列（影印版）74：微分方程數值方法引論 [Introduction to Numerical Methods in Differential Equations] 下載 mobi epub pdf txt 電子書

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