How can I integrate this ODE numerically?

[michujo]

Hello to everybody I'm trying to integrate this ODE but I don't know how:

f'''+a*f*f''=0 where a is a parameter.
With the boundary conditions f(0)=0; f(-inf)=1; f(inf)=1.

I had thought about using a shooting method but I don't know how to apply it with these boundary conditions. It would be nice if somebody could help me or give me a reference where I can find it( I have already looked for it in some books but I find nothing).

Thank you.

Michujo.

 

[michujo]

I'm sorry,there's a mistake in the boundary conditions. They are as follows:

f(0)=0; f'(inf)=1; f'(-inf)=(a-1)/a; where a is a parameter.