The formula has the form of an atracting fixed point if it looks like A=f(A) (and other conditions see the links below), then you can find the value of A by guessing an initial value A1:
A2=f(A1)
then try again
A3=f(A2)
and so on..
A(n+1)=f(A(n))
...
Eventually A(n) = A(n+1) and that's the fixed point solution.
In matlab you can make a function
function Phi2 = Phif(Re,Phi1)
% note the eq(3) is not quite Phi2=Phif(Re,Phi1), but ALMOST, just needs a
% little one step tweak
end
then call this function many times. The first call you guess a value, for the next calls you use the Phi2 output.
Instead of writing many calls just put the call in a loop and make the loop break when Phi1 is close enough to Phi2 (for example their absolute difference is very small)
when you get your asnwer, verify it by pluggin it in.
See:
