Solving an implicit equation (iteration)

I'm stuck at this question which is part of our chemical engineering comp lab. thanks in advance for your help.

Answer 1

[AndresVar]

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:

Fixed point (mathematics) - Wikipedia

real analysis - Why does this iterative way of solving an equation work? - Mathematics Stack Exchange

[Hammaad Shafi]

thank you for the response. I am still struggling on how to tweak equation 3 and how to start implementing the loop