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 uniformnon-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 linearnonlinear 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
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