Boundary value problem

[debrabr]

Hi,

First of all, thanks for any help.

I'm trying to solve a boundary value problem in Mathcad 14 by using ODEsolve function, but I have a problem. One of the two boundary conditions is of the form y(a)= constant. However, ODEsolve does not converge for some values of this constant, although I know the solution exists because this ODE has an analytical solution.

After my frustrated tentative, I try to solve by sbval function which the BVP becomes an IVP, but it doesn't work either.

I'm gonna send the file which has my solution. I appreciate any help.

Debra

[ptc-1368288]

>I know the solution exists because this ODE has an analytical solution.<<br> ________________________

Then why do you need Odesolve ?

Do you have the DE from source ? that you could plug as an image in the collab ? and the analytical solution as well. Your work sheet is restrictive to 14 users. Therefore, not clear if the problem is a version problem or a solving problem.

jmG

[TomGutman]

Guess values matter, and apparently the ODESolve has problems generating a usable guess value for the implied find.

Set up the problem to use the command line integrators and do your own boundary value solution (with a more reasonable guess value) and it works for larger values. There is still a limit, probably where the simple guess value used here is no longer adequate. A better guess value calculation might extend the range even further.

sbval should, with proper guess values, also work. But I can never remember how to use it, and it doesn't seem any simpler than the direct use of a solve block, so I don't usually bother with it.
__________________
� � � � Tom Gutman

[debrabr]

Then why do you need Odesolve ?

I��m trying to solve it by Mathcad just to compare the solutions since it��s like an exercise for another more complicated DE��s.
I was surprised when I realized this program doesn��t run to this simple equation (I��m trying to figure out if it��s my problem or a Mathcad��s bug)

Tom, actually, I��ve just started handling with Mathcad, so I can��t understanding quite well your solution, but I realized that for values over than ��supad=0.25 it doesn��t run either! I��m gonna try to understand and solve like you did!

Therefore, I tried solving by sbval function and it worked just for some values like the ODEsolve function, even changing the initial guess.

Thanks a lot

Debra

[TomGutman]

The problem is not the complexity (or lack thereof) of the equation, but the numeric stability (or lack thereof) of the solution. Your terminating condition is very sensitive to the initial condition, so you need a good guess value to be able to refine it. You might want to read up on chaos theory and ODE stability.

What aspect of my solution don't you understand? You can look up the functions I've used in the help (they are all built in Mathcad functions, I haven't included my usual utilities) and I can explain the usage if you have specific questions.

I don't understand about the .25. My solution works well above that, up to a bit above 1.4 (as can be seen in one of the plots.

What encoding are you using for your posts? It appears to be encoding special characters (like the apostrophe) as character pairs, but it's not the usual Unicode encoding (UTF-8) and my browser doesn't seem to recognize the encoding.
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� � � � Tom Gutman

[ptc-1368288]

>Then why do you need Odesolve ? <<br> ______________________________

I have recollection writing the question. You replied as an exercise, OK. DE's may have a very short life in the domain of the independent variable of integration. Did you carry the "uniqueness & existence Cauchy" and more: singular points. The boundary that you might figure may just be the quiz from the teacher.

jmG