I have these coupled equations based off Falkner-Skan:
f′′′=−f⋅f′′−(2m/(m+1))⋅(1−(f′)2)−(2/(m+1))⋅Ri⋅θcos(m/(m+1))
&
θ′′=−Pr⋅f⋅θ
With the BC's: f(0)=f′(0)=0 and θ(0)=1. f(5)=1 and θ(5)=0 (5 has been taken as the endpoint)
Where Pr, m and Ri are constants which can be assigned, f and θ are functions of η and the dash (') means derivative with respect to η.
I have a MATLAB file which solves this when Ri=0 by using the shooting method (as this is a BVP) and ODE45 but now it seems like that can no longer be used as easily because now they need to be solved simultaneously when Ri is not zero.
How can I solve this problem using MATLAB for the plots of f' and θ against η?