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;