降阶法及其在偏微分方程数值解中的应用（英文版）

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作　者：	Zhizhong Sun 著
出版社：	科学出版社
丛编项：
标　签：	微积分

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ISBN：	9787030245465	出版时间：	2009-06-01	包装：	平装
开本：	16开	页数：	415	字数：

内容简介

　　The layout of this book is as follows. Chapter 1 provides a microcosm of the method of order reduction via a two-point boundary value problem. Chapters 2， 3 and 4 are devoted， respectively， to the numerical solutions of linear parabolic， hyperbolic and elliptic equations by the method of order reduction. They are the core of the book. Chapters 5， 6 and 7 respectively consider the numerical approaches to the heat equation with an inner boundary condition， the heat equation with a nonlinear boundary condition and the nonlocal parabolic equation. Chapter 8 discusses the numerical approximation to a fractional diffusion-wave equation. The next five chapters are devoted to the numerical solutions of several coupled systems of differential equations. The numerical procedures for the heat equation and the Burgers equation in the unbounded domains are studied in Chapters 14， 15 and 16. Chapter 17 provides a numerical method for the superthermal electron transport equation， which is a degenerate and nonlocal evolutionary equation. The numerical solution to a model in oil deposit on a moving boundary is presented in Chapter 18. Chapter 19 deals with the numerical solution to the Cahn-Hilliard equation， which is a fourth order nonlinear evolutionary equation. The ADI and compact ADI methods for the multidimensional parabolic problems are discussed in Chapter 20. The numerical errors in the maximum norm are obtained. Chapter 21， the last chapter， is devoted to the numerical solution to the time-dependent SchrSdinger equation in quantum mechanics. ...

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图书目录

Chapter 1 The Method of Order Reduction .
1.1 Introduction
1.2 First order off-center difference method
1.3 Second order off-center difference method
1.4 Method of fictitious domain
1.5 Method of order reduction
1.6 Comparisons of the four difference methods
1.7 Conclusion
Chapter 2 Linear Parabolic Equations
2.1 Introduction
2.2 Derivative boundary conditions
2.3 Derivation of the difference scheme
2.4 A priori estimate for the difference solution
2.5 Solvability， stability and convergence
2.6 Two dimensional parabolic equations
2.7 Conclusion
Chapter 3 Linear Hyperbolic Equations
3.1 Introduction
3.2 Derivation of the difference scheme
3.3 A priori estimate
3.4 Solvability， stability and convergence
3.5 Numerical examples
3.6 Conclusion
Chapter 4 Linear Elliptic Equations
4.1 Introduction
4.2 Derivation of the difference scheme
4.3 Solvability， stability and convergence
4.4 The Neumann boundary value problem
4.5 A numerical example
4.6 Conclusion
Chapter 5 Heat Equations with an Inner Boundary Condition
5.1 Introduction
5.2 Derivation of the difference scheme
5.3 Solvability， stability and convergence
5.4 A numerical example
5.5 Conclusion
Chapter 6 Heat Equations with a Nonlinear Boundary Condition
6.1 Introduction
6.2 Derivation of the difference scheme
6.3 Convergence of the difference scheme
6.4 Unique solvability of the difference scheme
6.5 Iterative algorithm and a numerical example
6.6 Conclusion
Chapter 7 Nonlocal Parabolic Equations
7.1 Introduction
7.2 Derivation of the difference scheme
7.3 A prior estimate
7.4 Convergence and solvability
7.5 Extrapolation method
7.6 Implementation of the difference scheme
7.7 Conclusion
Chapter 8 Fractional Diffusion-wave Equations
8.1 Introduction
8.2 Approximation of the fractional order derivatives
8.3 Derivation of the difference scheme
8.4 Analysis of the difference scheme
8.5 A compact difference scheme
8.6 A slow diffusion system
8.7 A numerical example
8.8 Conclusion
Chapter 9 Wave Equations with Heat Conduction
9.1 Introduction
9.2 Boundary conditions
9.3 Derivation of the difference scheme
9.4 Solvability， stability and convergence
9.5 A practical recurrence algorithm
9.6 The degenerate problem
9.7 Conclusion
Chapter 10 Timoshenko Beam Equations with Boundary Feedback
10.1 Introduction
10.2 Derivation of the difference scheme ..
10.3 Analysis of the difference scheme
10.4 A numerical example
10.5 Conclusion.
Chapter 11 Thermoplastic Problems with Unilateral Constraint
11.1 Introduction
11.2 Derivation of the difference scheme
11.3 Stability and convergence
11.4 Numerical examples
11.5 Conclusion
Chapter 12 Thermoelastic Problems with Two-rod Contact
12.1 Introduction
12.2 Derivation of the difference scheme
12.3 Stability and convergence
12.4 Solvability and iterative algorithm
12.5 Numerical examples
12.6 Conclusion
Chapter 13 Nonlinear Parabolic Systems
13.1 Introduction
13.2 Difference scheme
13.3 Unique solvability and convergence
13.4 A numerical example
13.5 Conclusion
Chapter 14 Heat Equations in Unbounded Domains
14.1 Introduction
14.2 Derivation of the difference scheme
14.3 Analysis of the difference scheme
14.4 A numerical example
14.5 Conclusion
Chapter 15 Heat Equations on a Long Strip
15.1 Introduction
15.2 Derivation of the difference scheme
15.3 Analysis of the difference scheme
15.4 A numerical example
15.5 Conclusion
Chapter 16 Burgers Equations in Unbounded Domains
16.1 Introduction
16.2 Reformulation of the problem
16.3 Derivation of the difference scheme
16.4 Solvability and stability of the difference scheme
16.5 Convergence of the difference scheme
16.6 A numerical example
16.7 Conclusion
Chapter 17 Superthermal Electron Transport Equations
17.1 Introduction
17.2 Derivation of the difference scheme
17.3 Analysis of the difference scheme
17.4 A numerical example
17.5 Conclusion
Chapter 18 A Model in Oil Deposit
18.1 Introduction
18.2 Difference scheme and the main results
18.3 Derivation of the difference scheme
18.4 Solvability and convergence
18.5 Conclusion
Chapter 19 The Two-dimensional Cahn-Hillard Equation
19.1 Introduction
19.2 Derivation of the difference scheme
19.3 Solvability and convergence of the difference scheme
19.4 Conclusion
Chapter 20 ADI and Compact ADI Methods
20.1 Introduction
20.2 Notations and auxiliary lemmas
20.3 Error analysis of the ADI solution and its extrapolation
20.4 Error estimates of the compact ADI method
20.5 A numerical example
20.6 Conclusion
Chapter 21 Time-dependent SchrSdinger Equations
21.1 Introduction
21.2 One-dimensional Crank-Nicolson scheme
21.3 An extension to the high-order compact scheme
21.4 Extensions to multidimensional problems
21.5 Treatment of the nonhomogeneous boundary conditions
21.6 A numerical example
21.7 Conclusion
Bibliography