Solving system of PDE's 3

[EcoMan]

Our company has Mathcad, but I have never used it before. I'd like to solve a system of partial differential equations. Can anyone provide a Mathcad for Dummies step-by-step? Thank you.

 

[IRstuff]

You may want to look at the Mathcad Collaboratory, particularly the Calculus and DE forum:

http://collab.mathsoft.com/~Mathcad2000

You might also want to look at the Mathcad file library:

http://www.mathcad.com/Library/mathcad_files.asp

TTFN

 

[EcoMan]

Thank you for your reply. I searched the Mathcad library without success. I will put a post in the forum you suggested.

 

[IRstuff]

Did you look at the following electronic book in the Mathcad Library?

http://www.mathcad.com/library/ebooks/odesolve_toc.asp

TTFN

 

[EcoMan]

That was the only search result that seemed close but was for ordinary differential equations instead of PDE's. Maybe solving ODE's is not much different than solving PDE's? The book is on solving ODE's and DAE's. What is the difference between a DAE (differential algebraic equation?) and ODE?

 

[EcoMan]

I downloaded the 2001"i" book, but my version of Mathcad (2001 Professional) can't read it. The Mathcad Quicksheet "Solving a First-Order System of ODE's" might be good enough.

I find plenty of info on solving ODE's in Mathcad but am still not sure if solving PDE's with it is much different.

"A Differential Algebraic Equation (DAE) is an ordinary differential equation whose solution is subjected to additional equality constraints, not just initial or boundary conditions." (Mathcad)

 

[GregLocock]

It all depends on your boundary conditions.

in Mathcad 5+ you've got two choices, and you can only do 2D PDEs, zero on all edges or a consatnt on each edge. the help is pretty clear on all this, the functions used are multigrid and relax respectively.

I imagine that 2001 is backwards compatible with those commands, and intelligent use setting the defined points inside the grid should allow any boundary conditions you like (ie set up a patch inside the total solution that uses your boundary conditions for a few rows/columns)

Your initial suggestion of using Excel for this is a good one, I've occasionally thought about doing this, but you'll have to use a macro because you need circular references. Quattro or 123 would do it just using cell maths, as they used to allow circular references, and hence iterative calculations.



Cheers

Greg Locock

 

[peglor]

This might be a bit off topic, but Excel will allow you to use circular references. You have to turn on the iteration function on the Tools --> Options --> Calculations menu first though.

You can set it to iterate till the change is within a certain tolerance or to performa a certain number of interations (To work to a tolerance set the number of iterations to a high value and hope your claculations converge).

 

[EcoMan]

Thank you, Greg and peglor.

 

[mathemagician]

I would like to see the System of PDEs along with the
corresponding BCs, and Initial Conditions. The current
version of MathCAD,v11, has a very nice PDE-Block Solver.
The great progress in the area of PDE solvers started with
the previous release of MathCAD, 2001i, and that is
an ODE-Block Solver.

When I receive the system of PDEs, I will attempt to
set up the solution using my MathCAD v11 license. Incidentally, I have contributed to the ODE MathCAD
e-book available GRATIS for download and readable by
the previous version of MathCAD, v2001i, and the
current release, V11.