# How can i solve these systems of ODE

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samuel okeleye
on 21 Jan 2015

Commented: Zoltán Csáti
on 1 Apr 2015

(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

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### Accepted Answer

Zoltán Csáti
on 22 Jan 2015

##### 3 Comments

Zoltán Csáti
on 23 Jan 2015

Well, I recommend you the following.

- Download chebfun
- Install it
- Open it's GUI
- Type the equations
- Solve it

If you need any help, feel free to write.

### 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.

Sorry for not answering earlier, but the comments - in contrast to the answers - are not sent to my e-mail address.

##### 2 Comments

Zoltán Csáti
on 1 Apr 2015

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