Kutta's third order method has the coefficients
We want to use this method to find a stationary solution to the nonlinear Schrödinger equation
In order to find 
you have to insert the Ansatz for 
into the time-dependent equation above. This yields a second order ordinary differential equation for . Assuming that
as
we can find an analytic asymptotic expression for . From the asymptotic expression we can generate initial conditions for the ODE integration.
Write a program which implements the RK methods above to solve for .
Note: The solution for this problem can also be obtained analytically as
