numerical method
The set of coupled ordinary differential equations Eq. (8) and Eq. (9)
with boundary conditions Eq. (10) are computed numerically using
shooting method with Runge-Kutta Fehlberg integration scheme. This
method involves transforming the dimensionless coupled nonlinear
differential equations into a set of first order differential equations
after which, the fourth order Runge-Kutta Fehlberg integration scheme is
employed until the given boundary conditions are satisfied.
Thus, we define the new variables as;