Contents -- 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 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 -- 4.4 MHD flow 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 Conclusion -- 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.