The original ODE I had was $4f‴ + ff″ + 2(f′)² = 0$ with $f(0)=0, f′(0)=0$ & $f′(∞)=0$
I wish to use the 4th order Runge-Kutta method, so I have the system of three 1st order equation as below:
$$u′=v $$ $$v′=w $$ $$w′= - ¼uw -½v² $$
where $u=f, v=f′=df/dη, w=f″ $
and now the initial values are $u=0$ & $v=0$.
My problem is I am struggling to apply this method to my system of ODE's so that I can program a method that can solve any system of three first order ODE's. I would like for someone to please run through the step of the method, so I can understand it better. Optional: It would be very nice if anyone write down the MATLAB code for me.