How can i solve these systems of ODE
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(d^3 f)/(dη^3 )=-1/2.f(η).(d^2 f)/(dη^2 )-Grθ(η)…….. (1)
(d^2 θ)/(dη^2 )=-Pr.f(η). dθ/dη…………………….. (2)
(d^2 ϕ)/(dη^2 )=-1/2 Sc.f(η). dϕ/dη……….………… (3)
Gr, Sc and Pr are constants.
Domain is η from zero to infinity and I want the iteration to stop the moment the difference is 〖 10〗^(-6)
Boundary conditions f'(0)=0,θ(0)=1 and ϕ(0)=1 f'(∞)=1,θ(∞)=0 and ϕ(∞)=0
Zoltán Csáti on 22 Jan 2015
These are typical boundary layer equations. There are several strategies to tackle it. The two main solution methods: truncate it to some finite [0 L] interval or solve it on the semi-implicit domain. I recommend you the chebfun library because it is very easy to use. You can also use the built-in bvp4c function which is based on this article. There is also an example for the Falkner-Skan problem in it on page 16.
More Answers (1)
Zoltán Csáti on 31 Mar 2015
Well, you have to solve the system of BVPs several times for each different values of Gr, Pr and Sc. Then you can plot the data in one figure (see plot command) and can also add a legend. You may also put an arrow representing the effect of the different parameter values on the boundary layer. These can either be done programatically or by using the interactive tools.
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