Finite difference method with mathematica

Pasha Karami

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Oct 9, 2008, 6:39:16 AM10/9/08

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Dear all,

Does anybody know some examples or notebooks in Mathematica about finite
difference method for solving nonlinear PDEs?
I know about NDsolve which is not what I am looking for.I would like to
know about using Mathematica for finite difference method and etc.

Thank you!
Pasha

Jean-Marc Gulliet

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Oct 10, 2008, 4:35:40 AM10/10/08

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Pasha Karami wrote:

Google is your friend here: try googling "Mathematica finite difference
method PDE" (w/o the quotes). Among many other results, you could have a
closer look at,

"Module for Hyperbolic P.D.E.'s"
http://math.fullerton.edu/mathews/n2003/FiniteDifferencePDEMod.html

"Comparison of two different implementations of a
finite-difference-method for first-order pde in mathematica..."
http://arxiv.org/abs/cs.CE/0506051v1

"Math 221: Numerical Solution of Partial Differential Equations Part I"
http://www.amath.unc.edu/Faculty/mitran/courses/math221.html

Regards,
-- Jean-Marc

Tyler

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Oct 10, 2008, 4:37:37 AM10/10/08

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Not sure if it will help, but you might want to check out Michael
Trott's Guidebooks (either the symbolics, or numerics).

http://www.mathematicaguidebooks.org/

Of course, if you have the cash, there is an AceFEM package on the
Wolfram site you might want to look at.

As a side note, you may not want to implement a pure FE code in
Mathematica as you traditionally would in a procedural language like,
say, FORTRAN, or C. Solving these systems symbolically might make more
sense for some systems when using Mathematica. Having said that, I
myself am very new to Mathematica and have not coded any FE or FD
projects, so take that into consideration. Personally, I would love to
see a side-by-side solution of an FE system (even a simple 2D Heat
Eqn) in a procedural language like FORTRAN and the corresponding
solution in Mathematica.

Hope that gives you a starting point

t.

David Annetts

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Oct 11, 2008, 6:40:29 AM10/11/08

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Hi Pasha

> Does anybody know some examples or notebooks in Mathematica
> about finite difference method for solving nonlinear PDEs?
> I know about NDsolve which is not what I am looking for.I
> would like to know about using Mathematica for finite
> difference method and etc.

The IMTEK Library includes some finite difference routines.

Regards

Dave.

Tyler

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Oct 11, 2008, 6:43:13 AM10/11/08

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On Oct 10, 4:37 am, Tyler <hayes.ty...@gmail.com> wrote:
> Not sure if it will help, but you might want to check out Michael
> Trott's Guidebooks (either the symbolics, or numerics).
>
> http://www.mathematicaguidebooks.org/
>
> Of course, if you have the cash, there is an AceFEM package on the
> Wolfram site you might want to look at.
>
> As a side note, you may not want to implement a pure FE code in
> Mathematica as you traditionally would in a procedural language like,
> say, FORTRAN, or C. Solving these systems symbolically might make more
> sense for some systems when using Mathematica. Having said that, I
> myself am very new to Mathematica and have not coded any FE or FD
> projects, so take that into consideration. Personally, I would love to
> see a side-by-side solution of an FE system (even a simple 2D Heat
> Eqn) in a procedural language like FORTRAN and the corresponding
> solution in Mathematica.
>
> Hope that gives you a starting point
>
> t.
>
> On Oct 9, 6:39 am, "Pasha Karami" <kar...@geo.uu.nl> wrote:
>
> > Dear all,
>

> > Does anybody know some examples or notebooks in Mathematica about finit=

e
> > difference method for solving nonlinear PDEs?
> > I know about NDsolve which is not what I am looking for.I would like to
> > know about using Mathematica for finite difference method and etc.
>
> > Thank you!
> > Pasha

Also,

http://www.imtek.de/simulation//mathematica/IMSweb/

Nasser Abbasi

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Oct 11, 2008, 6:47:46 AM10/11/08

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"Tyler" <hayes...@gmail.com> wrote in message
news:gcn48h$74j$1...@smc.vnet.net...

> Personally, I would love to
> see a side-by-side solution of an FE system (even a simple 2D Heat
> Eqn) in a procedural language like FORTRAN and the corresponding
> solution in Mathematica.
>

For a school HW, this is a Mathematica implementation of finite difference
and finite element to compare the two numerical methods.

http://12000.org/my_courses/FULLERTON_COURSES/summer_2007/Math_503/HW/HW12/HW12_computer_part/index.htm

I have an Ada implementation (i.e. procedural) there as well for the same
problem (Finite element part) minus the GUI stuff as Ada does not have GUI
build-in as Mathematica does.

Nasser

dr DanW

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Oct 11, 2008, 6:49:00 AM10/11/08

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This probably goes way beyond what you are looking for, but there is
an open-source simulation toolbox for Mathematica at

http://www.imtek.de/simulation//mathematica/IMSweb/

It is very impressive; I wish I could understand and exploit 10% of
what this package looks capable of. You can use it to set up and
solve all kinds of node-based system equations, from analog circuits
to FEA.