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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