Solving differential equations

[Jarek83]

Hello,

I've got differential equations to solve. I've managed to solve it graphically and I can compute values for different arguments of functions.

Now I would like Mathcad to print formulas for resulting functions, or their approximations if getting exact formulas is not possible. Is there any way to do it?

Attached is a screenshot of my calculations. I will also provide a Mathcad 14 file if needed.

Thank you.

Best regards,
Jarek

 

[ishvaaag]

Maybe as you evaluate a(5) you can dump a number of solutions for specific abscissas and then use fitting functions to define curves that approach the results. Have not tried but try to feed a(v) with a vector of abscissas to see. If yes you can get a somewhat practical solution to the problem.

 

[Jarek83]

I have managed to solve the equations in Java using Apache Commons-Math package. It turned out to be a perfect solution for my needs.

The solution in Mathcad is most likely wrong as I should have not used odesolve which apparently works only for single equations.

Thanks for your time.

 

[excognito]

>> I have managed to solve the equations in Java using Apache Commons-Math package. It turned out to be a perfect solution for my needs.

Out of interest, what functions in the Common Maths package did you use. AFAICT from a quick glance, the CM package is purely numeric and doesn't offer symbolic solutions.

== The solution in Mathcad is most likely wrong as I should have not used odesolve which apparently works only for single equations.

odesolve works on multiple equations and I've seen some pretty complex worksheets that use odesolve. If the solution is wrong, it's more likely there is an error in its formulation.

 

[Jarek83]

I used GraggBulirschStoerIntegrator. And yes, it is numeric, however a standalone application that solves the equations to get final results is exactly what I needed. My initial intention was to take the symbolic solution from Mathcad and use it in my application. I know, this is a completely wrong approach to the problem, I should have thought of numeric libraries earlier.

I know the solution in Mathcad is wrong because it doesn't match numbers given in a book I got the equations from. On the other hand results produced by my Java application do match. So it is probably as you say, something must be wrong with the usage of odesolve.

On a side note, in the aforementioned book a symbolic solution was also given but some of intermediate formulas produce complex numbers while the final solution is supposed to be real. I have contacted the author and he had no idea how he had got the real solution a dozen years or so ago

 

[PNachtwey]

I could not get a symbolic answer using Mathcad but I could find formulas for a(t), b(t) and d(t). I used a different approach.

http://www.deltamotion.com/peter/Mathcad/Mathcad - Jarek83.pdf

It is hard for Mathcad and wxMaxima to find the inverse Laplace transform when using symbolics. I bet a CAS like Mathematica could do it.

Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

 

[Jarek83]

Peter,

This is very interesting. Thank you very much!