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In this chapter, we discuss the application of the Keller-box method to solve more advanced coupled nonlinear boundary value problems of one or more independent variables. In Sections 6.1 and 6.3, the effects of variable fluid properties on the boundary layer flow and heat transfer of a fluid over a flat sheet are studied; whereas in Section 6.2, we study dusty fluid flow over a stretching sheet. The hydromagnetic mixed convection boundary layer flow of an electrically conducting fluid over a non-isothermal wedge and sphere under different physical situations are analyzed in Sections 6.4 and 6.5. In Section 6.6, we study the flow and heat transfer of an electrically conducting viscoelastic fluid past a semi-infinite plate.

In this chapter, we introduce the basic principles of finite difference methods for solving a system of linear homogeneous first order differential equations. In Section 2.2, we solve the second and higher order linear/nonlinear differential equations using different types of boundary conditions; we also obtain convergence and stability results. In Section 2.3 we briefly explain the finite difference method, shooting method, and the Keller-box method.