What is the solution of this? 2nd part

[Clausius2]

Hi Max,

Thanks very much, but now I am puzzled solving this problem:

F'''+FF''/2=0

F'(-infinite)=1
F(-infinite)=0
F'(infinite)=0

I am looking for a numerical solution, and I have been trying unsuccesfully to understand the non-linear shooting method, in order to code it with Matlab.

Be a good man, Max, and help an ODE's world wanderer.

 

[Max0526]

hi

Hi, Clausius2;

> I am looking for a numerical solution, and I have been trying unsuccesfully
> to understand the non-linear shooting method, in order to code it with
> Matlab.

Is it a goal to code it in Mathlab, or you just need to code it somewhere? And why non-linear shooting method? Why not standard RK4 (Runge-Kutta of the 4th order)?
To say the truth, I don't know Mathlab at all. Sorry for the stupid suggestion, but have you tried to find a ready Mathlab program in the Internet for any DE (system of DEs)? Try here for example: http://www.math.umn.edu/~olver/matlab.html.
Then, why not rewrite the original DE as three first-order DEs and solve that system? I did this, but it was 100 years ago and I programmed in QuickBasic.

> Be a good man, Max, and help an ODE's world wanderer.

I would like to, but I'm mostly interested in _analytic_ solutions. And this particular equation is _very_ interesting since they say it cannot be completely integrated analytically (http://mathworld.wolfram.com/BlasiusDifferentialEquation.html).
If I find smth related to your problem, I'll post it here.

Best of luck,
Max.

 

[Max0526]

check this

Clausius2,
check this link for using Mathlab for solving of ODEs:
http://math.rice.edu/~polking/odesoft/dfpp.html,
and these ones for numerical solving of ODEs in general:
http://mathlab.cit.cornell.edu/math_software_resources/math_software_resources.html,
http://archives.math.utk.edu/software/msdos/diff.equations/.html.
Best of luck,
Max.

P.S. Well, man. It seems to me that I found the description of integration of the problem similar to yours. Read
Example: Using Continuation to Verify a Solution's Consistent Behavior
right here: http://www.mathworks.com/access/helpdesk/help/techdoc/math_anal/diffeq22.html#709310 .
Input beta=0, 1/2 in front of y*y'' and change the BCs and that seems to be it.
Check this link just in case: http://www.mathworks.com/access/helpdesk/help/techdoc/math_anal/math_anal_example_index.html .

 

[Max0526]

more links

Hi, man;
Check these links as well:
http://www.chem.mtu.edu/~jmkeith/cm3120/matlab/blasius.m
http://www-iwse.eng.ohio-state.edu/ISEStudents/xue/coursework/ME%20705/p2.htm
http://www.ma.man.ac.uk/~ajuel/teaching/BL03notes5.pdf
http://www.aeronautics.hut.fi/edu/kurssit/130/Luento_04.pdf
http://www.people.virginia.edu/~rjr/modules/xls/
http://www.people.virginia.edu/~rjr/modules/xls/HTTblasius.xls
http://www.me.iastate.edu/me536_battaglia/Lectures/Part12.pdf
Best of luck,
Max.

 

[Clausius2]

Thanks

Thank you so much, Max.

I'm sure your links will be very useful. Now I am with my final exams, so I will come back to this problem on July.

What a pity you are not a woman, because I would ask you to marry with me. :rofl: