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Topic: Third order non-linear boundary value problem
Replies: 7   Last Post: Apr 2, 2014 12:34 PM

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 Gene Posts: 35 Registered: 11/2/07
Re: Third order non-linear boundary value problem
Posted: Mar 28, 2014 9:59 AM

"Rachel " <rachel-dore20@hotmail.com> wrote in message <lh1o34\$9lh\$1@newscl01ah.mathworks.com>...
> Hey guys,
>
> I'm having a lot of trouble trying to get a numerical solution the the following boundary value problem,
>
> f'''+1/3ff''+1/3f'^2=0
>
> with the following boundary conditions,
>
> eta=0, f=0 & f''=0
> eta=infintiy, f'=0
>
> I am new to Matlab and I'm completely lost so your help would be much appreciated. I think this is how I set it up but I'm not sure??
>
> function dfdeta = mat4ode(eta,f)
> dfdeta = [ f(2)
> f(3)
> -1/3*f(1)*f(3)-1/3*Y(2)*Y(2) ];
>
> and for the boundary conditions,
>
> function res = mat4bc(ya,yb)
> res = [ ya(3)
> ya(1)
> yb(2)];
>
> And this is an attempt at the rest the code,
>
> function mat4bvp(solver)
>
> if nargin < 1
> solver = 'bvp4c';
> end
> bvpsolver = fcnchk(solver);
>
> infinity = 3;
>
> solinit = bvpinit(linspace(0,infinity,5),[0,0,0]);
>
> sol = bvpsolver(@mat4ode,@mat4bc,solinit);
>
> eta = sol.x;
> f = sol.y;
>
> figure(1)
> plot(eta,f)
> legend('F_1', 'F_2', 'F_3', 3)
> grid
>
> end
>
> I would be very grateful for the help. Thanks a mill.
>
> Rachel

Hi Rachel:

I believe your ODE can be re-written as
f''' + (1/3) (f f')' = 0
which integrates to
f'' + (1/3) (f f') = C
Your b.c. imply C = 0
The 2nd order system also admits a first integral
f' + (1/6) f^2 = C;
again the b.c. imply C = 0
The result is now 1st order and separable.

gene

Date Subject Author
3/27/14 Rachel
3/28/14 Torsten
3/28/14 Rachel
3/28/14 Torsten
3/28/14 Rachel
4/2/14 Rachel
3/28/14 Gene
3/28/14 Rachel