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dont
03-13-2007, 01:37 PM
I have been using this software for quite a while now. Normally I write my own code, but I hit a few snags.

Elliptic problems with partial boundary conditions.

Problems which just would not solve quickly or accurately using finite difference methods.

Also I had had time dependent problems whose initial condition was a delta function.

Granville Sewell is extremely helpful, and his numerical insights are often ground breaking.

His software is very recommended.
Don't be fooled by the lack of a slick interface, this is serious software.

Adriana
03-13-2007, 08:02 PM
PDE2D is not only serious Software but also a compatible Program with Matlab!!!
One can get the *.m file for Matlab in an instantaneous way in the course of PDE2D run and so computes beautiful plots.

"Granville Sewell is extremely helpful, and his numerical insights are often ground breaking" --> I agree with You totally!!! :)


Adriana.

dadudek
03-13-2007, 10:49 PM
PDE2D was a key tool used in my graduate research, solving systems of 7 to 15 simultaneous partial differential and algebraic equations in two dimensions. I found the program to be superior in several ways, compared to other solvers:

1) PDE2D was able to solve problems that other solvers were not able to solve when given identical initial guesses
2) PDE2D was able to solve the same problem faster than other solvers when both solvers were able to converge to the solution
3) PDE2D has an interface that is designed to help the user get started without reading manuals, etc. This interface results in an input file that the solver uses to define the problem, initial conditions, boundary conditions, etc. Obviously, all solvers will have a method to input problem parameters, but PDE2D is really quite flexible because the input file that is generated can be directly edited by the user to accomidate atypical circumstances.
4) PDE2D cooperates well with MATLAB, and can output results to m-files.
5) Lastly, and this one is important, the author of the software is the person who will answer your emails and help you get going to solve the problems you are interested in. In addition to being an obviously bright guy, Granville is genuinely intersted in helping you, and responds to queries remarkably quickly. It is like having a math professor (did you know he is Professor at University of Texas-El Paso?) helping you set up and solve your systems of equations.

The previous poster called this "serious software", and I agree. If you have systems of differential equations to solve, consider PDE2D. I was impressed and suspect you will be too. :)

sewell
04-14-2007, 11:04 AM
"dont" didn't mention this, but he is using PDE2D for some math finance applications. This is an application area where PDE2D has a clear advantage over competing general-purpose programs, because in addition to the Galerkin finite element method (also provided by competing programs) it offers a collocation finite element method option. The Galerkin method requires the user to put his/her PDEs and boundary conditions into a "divergence" format, which is perfectly appropriate for many science and engineering applications, but it is awkward and inconvenient, and occasionally even impossible, to convert math finance applications into this form. (See "The PDE2D collocation methods" at www.pde2d.com for more details.) The Galerkin method is preferred when the region is complicated, but math finance applications are usually solved on rectangles or other simple regions.

Juergen Topper used PDE2D throughout his book, "Financial Engineering with Finite Elements," John Wiley & Sons, 2005 (www.vni.com/products/affiliated/PDE2D_ProductPage.html for a link to this book), to solve a wide range of applications. Dr. Topper made the following comment about PDE2D:

"PDE2D is a very flexible and powerful tool for solving differential equations arising in finance and economics in general. It is fairly easy to use; the support by Prof. Sewell is outstanding. I have used PDE2D mainly to compute fair values and hedging parameters of exotic options in the equity and FX market. So far, every problem could be solved with PDE2D to my full satisfaction."