Iterating to ODEsolve soltution (shooting method)

[JM_14109889]

I am using Mathcad Prime Release 8.0 and Datecode8.0.0.0

I want to add an iteration process to an ODEsolve block. It would require iterating an initial condition until two of the solutions match.

[DhirajPatil]

hi @JM_14109889, 

Can you please share a sample worksheet? 

Regards,

Dhiraj 

[JM_14109889]

Hi @DhirajPatil ,

See attached worksheet.  This worksheet has been simplified down to the basic equations.  Currently I am required to iterate variables until the solution of both equations is equal at "L" (T1(L)=T2(L).  All variables could potentially be iterated to achieve the solution, but most common would be T1(0) or U1.

Thanks.  

[JM_14109889]

Hi, I have shared the sample worksheet.

[LucMeekes · Accepted solution]

Answer: T1(0)=202.446 °C

Your problem:

Solve the set of ODE:

Extract the functions:

Check that it's the solution:

Solve the problem to find T10 for T1(L)=T2(L):

Fill in the numbers:

Plot:

Note that Prime 9 and higher (present version is 11) can solve your set of DE symbolically, allowing you to through above exercise.

You can, (in your Prime 8 ) make the solve block be a function of T10 and then numerically solve it. For a simple example see: https://community.ptc.com/t5/Mathcad/Solve-Block-Iteration/m-p/889162 

This forum (part) is for installation and licensing problems. For more help, post your problem in the proper forum (part): https://community.ptc.com/t5/Mathcad/bd-p/PTCMathcad 

Success!
Luc

[JM_14109889]

Thanks for the reply.  If I'm understanding correctly, I need to upgrade my MathCad version to make use of the above solution.

[LucMeekes]

That is one way. As usual there are several ways (to Rome). So you can also do it the numeric way, by making the result of the solve-block a (set of) function(s) in T10, after which you can solve for the proper T10-value that makes T1(L)=T2(L).

You can also use the symbolics available in Prime 8 to compute the solution via the Laplace transform, which changes the set of ODE into a set of equations, which you solve and then transform back to the x-domain.

That goes like this:

Now with results

Note that in Prime the result may have the laplace integral (definition)

(  Something like    )

instead of "laplace(T1(x),x,s)" and "laplace(T2(x),x,s)" so you may have to change the substitution below for your needs.

Simplify:

The functions may become big, but they should still be workable.

Success!
Luc

[JM_14109889]

Thanks!