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，在强非线性问题前显得力不从心。瓦捷拉维鲁、普拉萨德著的《Keller-Box方法及其应用(精)》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(精)》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，后半部分则给出了大量的在流体领域用Keller－Box方法解决的非线性问题的实例。
在瓦捷拉维鲁、普拉萨德著的《Keller-Box方法及其应用(精)》中，我们强调的发展和有限差分技术的应用分析，凯勒箱法为解决方案的耦合非线性边界值问题。这本书对那些有兴趣的凯勒箱法作为一个工作为解决物理和工程问题的工具。这本书可以帮助读者开发工具包的申请所需的方法进行筛选。，有很多的应用在文献中的凯勒盒方法阳离子的选择应用。并通过具体的问题，我们已经限制了。*注意流体流动和传热现象。因此，为了说明各种有用的应用凯勒箱法在性质和工具，我们有了这次的研究成果。
chapter 0 introduction
References
Chapter 1 basics of the finite difference approximations
1.1finite difference approximations
1.2the initial value problem for odes
1.3some basic numerical methods
1.4some basic pdes
1.5numerical solution to partial differential equations
references
Chapter 2 principles of the implicit keller-box method
2.1principles of implicit finite difference methods
2.2finite difference methods
2.3boundary value problems in ordinary differential equations
references
Chapter 3 stability and convergence of the implicit keller-box methodchapter 0 introduction
References
Chapter 1 basics of the finite difference approximations
1.1finite difference approximations
1.2the initial value problem for odes
1.3some basic numerical methods
1.4some basic pdes
1.5numerical solution to partial differential equations
references
Chapter 2 principles of the implicit keller-box method
2.1principles of implicit finite difference methods
2.2finite difference methods
2.3boundary value problems in ordinary differential equations
references
Chapter 3 stability and convergence of the implicit keller-box method
3.1convergence of implicit difference methods for parabolic functional differential equations
3.1.1introduction
3.1.2discretization of mixed problems
3.1.3solvability of implicit difference functional problems
3.1.4approximate solutions of difference functional problems
3.1.5convergence of implicit difference methods
3.1.6numerical examples
3.2rate of convergence of finite diffrence scheme on uniform/non-uniform grids
3.2.1introduction
3.2.2analytical results
3.2.3numerical results
3.3stability and convergence of crank-nicholson method for fractional advection dispersion equation
3.3.1introduction
3.3.2problem formulation
3.3.3numerical formulation of the crank-nicholson method
3.3.4stability of the crank-nicholson method
3.3.5convergence
3.3.6radial flow problem
3.3.7conclusions
references
Chapter 4 application of the keller-box method to boundary layer problems
4.1flow of a power-law fluid over a stretching sheet
4.1.1introduction
4.1.2formulation of the problem
4.1.3numerical solution method
4.1.4results and discussion
4.1.5concluding remarks
4.2hydromagnetic flow of a power-law fluid over a stretching sheet
4.2.1introduction
4.2.2flow analysis
4.2.3numerical solution method
4.2.4results and discussion
4.3mhd power-law fluid flow and heat transfer over a non-isothermal stretching sheet
4.3.1introduction
4.3.2governing equations and similarity analysis
4.3.3heat transfer
4.3.4numerical procedure
4.3.5results and discussion
4.4mhd glow and heat transfer of a maxwell fluid over a non-isothermal stretching sheet
4.4.1introduction
4.4.2mathematical formulation
4.4.3heat transfer analysis
4.4.4numerical procedure
4.4.5results and discussion
4.4.6conclusions
4.5mhd boundary layer flow of a micropolar fluid past a wedge with constant wall heat flux
4.5.1introduction
4.5.2flow analysis
4.5.3flat plate problem
4.5.4results and discussion
4.5.5conclusions
references
Chapter 5 application of the keller-box method to fluid flow and heat transfer problems
5.1hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet
5.1.1introduction
5.1.2mathematical formulation
5.1.3solution of the problem
5.1.4results and discussion
5.1.5conclusions
5.2convection flow and heat transfer of a maxwell fluid over a non-isothermal surface
5.2.1introduction
5.2.2mathematical formulation
5.2.3skin friction
5.2.4nusselt number
5.2.5results and discussion
5.2.6conclusion
5.3the effects of variable fluid properties on the hydromagnetic flow and heat transfer over a nonlinearly stretching sheet
5.3.1introduction
5.3.2mathematical formulation
5.3.3numerical procedure
5.3.4results and discussion
5.3.5conclusions
5.4hydromagnetic flow and heat transfer of a non-newtonian power law fluid over a vertical stretching sheet
5.4.1introduction
5.4.2mathematical formulation
5.4.3numerical procedure
5.4.4results and discussion
5.5the effects of linear/nonlinear convection on the non-darcian flow and heat transfer along a permeable vertical surface
5.5.1introduction
5.5.2mathematical formulation
5.5.3numerical procedure
5.5.4results and discussion
5.6unsteady flow and heat transfer in a thin film of ostwald-de waele liquid over a stretching surface
5.6.1introduction
5.6.2mathematical formulation
5.6.3numerical procedure
5.6.4results and discussion
5.6.5conclusions
references
Chapter 6 application of the keller-box method to more advanced problems
6.1heat transfer phenomena in a moving nanofluid over a horizontal surface
6.1.1introduction
6.1.2mathematical formulation
6.1.3similarity equations
6.1.4numerical procedure
6.1.5results and discussion
6.1.6conclusion
6.2hydromagnetic fluid flow and heat transfer at a stretching sheet with fluid-particle suspension and variable fluid properties
6.2.1introduction
6.2.2mathematical formulation
6.2.3solution for special cases
6.2.4analytical solution by perturbation
6.2.5numerical procedure
6.2.6results and discussion
6.2.7conclusions
6.3radiation effects on mixed convection over a wedge embedded in a porous medium filled with a nanofluid
6.3.1introduction
6.3.2problem formulation
6.3.3numerical method and validation
6.3.4results and discussion
6.3.5conclusion
6.4mhd mixed convection flow over a permeable non-isothermal wedge
6.4.1introduction
6.4.2mathematical formulation
6.4.3numerical procedure
6.4.4results and discussion
6.4.5concluding remarks
6.5mixed convection boundary layer flow about a solid sphere with newtonian heating
6.5.1introduction
6.5.2mathematical formulation
6.5.3solution procedure
6.5.4results and discussion
6.5.5conclusions
6.6flow and heat transfer of a viscoelastic fluid over a flat plate with a magnetic field and a pressure gradient
6.6.1introduction
6.6.2governing equations
6.6.3results and discussion
6.6.4conclusions
References
Subject index
Author index
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