Are there any specialized Computer Algebra Systems (or packages for these) for finding closed form solutions to
a) partial differential equations, b) stochastic differential equations?
If yes, what experiences do you have with these?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
|
1
2
|
|
||
|
|
|
2
|
I have used Wolfram Mathematica extensively in my undergraduate course so far. Although the PDEs and systems of PDEs I have encountered have not been overly complicated, Mathematica is able to solve them in closed form most of the time. While not a "specialised" CAS for PDEs/SDEs, it gave me the closed form solutions I was looking for. This link may be useful in terms of gauging what you can do. |
||
|
|
You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.
|
3
|
Most ODEs, nevermind PDEs and SDEs don't have what one would usually call "closed form" solutions. Are you interested in a special class of equations (e.g. linear, constant coefficient, on flat manifolds without boundary) for which closed form solutions are likely to exist? |
|||
|
|
1
|
For PDEs, the PDEtools package in Maple might be of use. I don't know exactly which types of PDEs it can solve, but the author and maintainer of this package, Edgardo Cheb-Terrab, has a background in theoretical physics, so I suspect that is its main emphasis. |
||
|
|
|
0
|
For usual (non-stochastic) PDEs indeed consider giving Maple a try. You don't even have to bother too much with the PDEtools package, just try Maple's command pdsolve and see for yourself. |
||
|
|
