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。我们的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。

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。

chapter 0 introduction

References

Chapter 1 basics of the finite difference 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 diffrence 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

 4.4 mhd glow and heat transfer of a maxwell fluid over a non-isothermal stretching sheet

4.4.1 introduction

4.4.2 mathematical formulation

4.4.3 heat transfer analysis

4.4.4 numerical procedure

4.4.5 results and discussion

4.4.6 conclusions

 4.5 mhd boundary layer flow of a micropolar fluid past a wedge with constant wall heat flux

4.5.1 introduction

4.5.2 flow analysis

4.5.3 flat plate problem

4.5.4 results and discussion

4.5.5 conclusions

 references

Chapter 5 application of the keller-box method to fluid flow and heat transfer problems

 5.1 hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet

5.1.1 introduction

5.1.2 mathematical formulation

5.1.3 solution of the problem

5.1.4 results and discussion

5.1.5 conclusions

 5.2 convection flow and heat transfer of a maxwell fluid over a non-isothermal surface

5.2.1 introduction

5.2.2 mathematical formulation

5.2.3 skin friction

5.2.4 nusselt number

5.2.5 results and discussion

5.2.6 conclusion

 5.3 the effects of variable fluid properties on the hydromagnetic flow and heat transfer over a nonlinearly stretching sheet

5.3.1 introduction

5.3.2 mathematical formulation

5.3.3 numerical procedure

5.3.4 results and discussion

5.3.5 conclusions

 5.4 hydromagnetic flow and heat transfer of a non-newtonian power law fluid over a vertical stretching sheet

5.4.1 introduction

5.4.2 mathematical formulation

5.4.3 numerical procedure

5.4.4 results and discussion

 5.5 the effects of linear/nonlinear convection on the non-darcian flow and heat transfer along a permeable vertical surface

5.5.1 introduction

5.5.2 mathematical formulation

5.5.3 numerical procedure

5.5.4 results and discussion

 5.6 unsteady flow and heat transfer in a thin film of ostwald-de waele liquid over a stretching surface

5.6.1 introduction

5.6.2 mathematical formulation

5.6.3 numerical procedure

5.6.4 results and discussion

5.6.5 conclusions

 references

Chapter 6 application of the keller-box method to more advanced problems

 6.1 heat transfer phenomena in a moving nanofluid over a horizontal surface

6.1.1 introduction

6.1.2 mathematical formulation

6.1.3 similarity equations

6.1.4 numerical procedure

6.1.5 results and discussion

6.1.6 conclusion

 6.2 hydromagnetic fluid flow and heat transfer at a stretching sheet with fluid-particle suspension and variable fluid properties

6.2.1 introduction

6.2.2 mathematical formulation

6.2.3 solution for special cases

6.2.4 analytical solution by perturbation

6.2.5 numerical procedure

6.2.6 results and discussion

6.2.7 conclusions

 6.3 radiation effects on mixed convection over a wedge embedded in a porous medium filled with a nanofluid

6.3.1 introduction

6.3.2 problem formulation

6.3.3 numerical method and validation

6.3.4 results and discussion

6.3.5 conclusion

 6.4 mhd mixed convection flow over a permeable non-isothermal wedge

6.4.1 introduction

6.4.2 mathematical formulation

6.4.3 numerical procedure

6.4.4 results and discussion

6.4.5 concluding remarks

 6.5 mixed convection boundary layer flow about a solid sphere with newtonian heating

6.5.1 introduction

6.5.2 mathematical formulation

6.5.3 solution procedure

6.5.4 results and discussion

6.5.5 conclusions

 6.6 flow and heat transfer of a viscoelastic fluid over a flat plate with a magnetic field and a pressure gradient

6.6.1 introduction

6.6.2 governing equations

6.6.3 results and discussion

6.6.4 conclusions

References

Subject index

Author index