OdeSolve for 2 point BVP

[JohnRudnicki]

I am trying to solve a two point boundary value problem. Instead of three initial conditions for the problem, I am giving the value at the end of the solution interval. Can I use odesolve? My initial attempt (below and in attached worksheet) was not successful. If not what else? I have not solved this type of problem before. I know "shooting methods" are one possible approach, but I do not know how to set this up in MC. Any help would be appreciated. FYI I am using MC14, but saved the sheet as MC 11.  Thanks.

[rgunwaldsen · Accepted solution]

You might consider the attached PDF article from Dr. Tom Co 11/3/2008. Mathcad 15 and Prime 8 worksheets attached.

[rgunwaldsen]

Here's another approach using Laplace transforms. I think original content is courtesy of Luc Meekes.

[JohnRudnicki]

Thanks. I will take a look.

[JohnRudnicki]

bvp.pdf and BVP_15.xmcd were very helpful, but I could not open the *.mcdx files. What kind of mc files are they. (Not sure the Laplace transform approach will work since the problem is non-linear). 

[JohnRudnicki]

Sorry. Never mind. Just saw they were prime files and downloaded Prime to open. Thanks again.

[LucMeekes]

I had to rewrite the differential equations, or Mathcad 11 would not understand. (It seems it likes the highest order differential on the LHS better).

Then a little experimenting gives:

Is that close enough for you?

Success!
Luc

[JohnRudnicki]

Yes! Nice. Thanks. John

[Werner_E]

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@LucMeekes wrote:

Is that close enough for you?

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If its not close enough then the value for w10 can be improved by turning the solve block into a function of w10 and use either another solve block or the root() function to get the 'optimal' value for w10 within Mathcad's numeric precision.

[JohnRudnicki]

Thanks. Good to know.