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Keller-Box方法及其应用（英文版）
作者：（美）瓦捷拉维鲁（Vajravelu,K.），（印）普拉萨德（Prasad,K.V.）著
出版社：高等教育出版社
出版时间：2014-01-01
ISBN：9787040388916
定价：¥89.00
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内容简介
科学和工程中大部分问题都是非线性的，这些问题难以解决。传统的分析近似只对弱非线性问题有效，在强非线性问题前则显得力不从心。《Keller-Box 方法及其应用（英文版）》介绍了针对非线性问题非常有效的Keller-Box方法的最新理论发展和应用。《Keller-Box 方法及其应用（英文版）》前半部分讲述了一些基本的概念，用以帮助读者理解该方法的理论框架，后半部分则给出了该方法在流体领域解决非线性问题的大量实例。Kuppalapalle Vajravelu是美国中佛罗里达大学数学，力学、材料以及航空和航天工程教授，研究领域为非线性方程、非线性力学、热传导、数值分析、同伦分析方法等，是Differential Equations and Nonlinear Mechanics的创刊主编。
作者简介
暂缺《Keller-Box方法及其应用（英文版）》作者简介
目录
Chapter 0 Introduction
References
Chapter 1 Basics of the Finite DifIFerence Approximations
1.1 Finite difference approximations
1.2 The initial value problem for ODEs
1.3 Some basic numerical methods
1.4 Some basic PDEs
1.5 Numerical solution to partial differential equations
References
Chapter 2 Principles of the Implicit Keller-box Method
2.1 Principles of implicit finite difference methods
2.2 Finite difference methods
2.3 Boundary value problems in ordinary differential
equations
References
Chapter 3 Stability and Convergence of the Implicit Keller-box Method
3.1 Convergence of implicit difference methods for parabolic functional differential equations
3.1.1 Introduction
3.1.2 Discretization of mixed problems
3.1.3 Solvability of implicit difference functional problems
3.1.4 Approximate solutions of difference functional problems
3.1.5 Convergence of implicit difference methods
3.1.6 Numerical examples
3.2 Rate of convergence of finite difference scheme on uniform/non-uniform grids
3.2.1 Introduction
3.2.2 Analytical results
3.2.3 Numerical results
3.3 Stability and convergence of Crank-Nicholson method for fractional advection dispersion equation
3.3.1 Introduction
3.3.2 Problem formulation
3.3.3 Numerical formulation of the Crank-Nicholson method
3.3.4 Stability of the Crank-Nicholson method
3.3.5 Convergence
3.3.6 Radial flow problem
3.3.7 Conclusions
References
Chapter 4 Application of the Keller-box Method to Boundary Layer Problems
4.1 Flow of a power-law fluid over a stretching sheet
4.1.1 Introduction
4.1.2 Formulation of the problem
4.1.3 Numerical solution method
4.1.4 Results and discussion
4.1.5 Concluding remarks
4.2 Hydromagnetic flow of a power-law fluid over a stretching sheet
4.2.1 Introduction
4.2.2 Flow analysis
4.2.3 Numerical solution method
4.2.4 Results and discussion
4.3 MHD Power-law fluid flow and heat transfer over a non-isothermal stretching sheet
4.3.1 Introduction
4.3.2 Governing equations and similarity analysis
4.3.3 Heat transfer
4.3.4 Numerical procedure
4.3.5 Results and discussion
……
Chapter 5 Application of the Keller-box Method to Fluid Flow and Heat rlyansfer Problerus
Chapter 6 Application of the Keller-box Method to More Advanced Problems
Subject Index
Author Index
References
Chapter 1 Basics of the Finite DifIFerence Approximations
1.1 Finite difference approximations
1.2 The initial value problem for ODEs
1.3 Some basic numerical methods
1.4 Some basic PDEs
1.5 Numerical solution to partial differential equations
References
Chapter 2 Principles of the Implicit Keller-box Method
2.1 Principles of implicit finite difference methods
2.2 Finite difference methods
2.3 Boundary value problems in ordinary differential
equations
References
Chapter 3 Stability and Convergence of the Implicit Keller-box Method
3.1 Convergence of implicit difference methods for parabolic functional differential equations
3.1.1 Introduction
3.1.2 Discretization of mixed problems
3.1.3 Solvability of implicit difference functional problems
3.1.4 Approximate solutions of difference functional problems
3.1.5 Convergence of implicit difference methods
3.1.6 Numerical examples
3.2 Rate of convergence of finite difference scheme on uniform/non-uniform grids
3.2.1 Introduction
3.2.2 Analytical results
3.2.3 Numerical results
3.3 Stability and convergence of Crank-Nicholson method for fractional advection dispersion equation
3.3.1 Introduction
3.3.2 Problem formulation
3.3.3 Numerical formulation of the Crank-Nicholson method
3.3.4 Stability of the Crank-Nicholson method
3.3.5 Convergence
3.3.6 Radial flow problem
3.3.7 Conclusions
References
Chapter 4 Application of the Keller-box Method to Boundary Layer Problems
4.1 Flow of a power-law fluid over a stretching sheet
4.1.1 Introduction
4.1.2 Formulation of the problem
4.1.3 Numerical solution method
4.1.4 Results and discussion
4.1.5 Concluding remarks
4.2 Hydromagnetic flow of a power-law fluid over a stretching sheet
4.2.1 Introduction
4.2.2 Flow analysis
4.2.3 Numerical solution method
4.2.4 Results and discussion
4.3 MHD Power-law fluid flow and heat transfer over a non-isothermal stretching sheet
4.3.1 Introduction
4.3.2 Governing equations and similarity analysis
4.3.3 Heat transfer
4.3.4 Numerical procedure
4.3.5 Results and discussion
……
Chapter 5 Application of the Keller-box Method to Fluid Flow and Heat rlyansfer Problerus
Chapter 6 Application of the Keller-box Method to More Advanced Problems
Subject Index
Author Index
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