The approximation for the boundary layer theory drives to the set of Prandtl equations. The momentum equation, combined with the continuity equation can be rewritten using the von Mises transformation in a parabolic equation where the x direction is a time-like direction.

Now you can use a very simple discretization for parabolic equations using explicit or implicit methods. The first try would be a first order discretization in x and a second order in y. For the implicit method you simply get the three coefficients for the tridiagonal matrix.

Thank you dear Filippo Maria Denaro ! Okay sir I am gonna check out the implicit method and see how it works !

Vielen Dank !

Good work