I love that you're working on this. I've tried to give some suggestions that might help.
On Jun 27, 2009, at 9:53 AM, Priit Laes wrote: > > Hey! > > I have pushed a branch which contains code to handle some forms of > separable partial equations. > > I have currently only implemented basic support for multiplicative > separate case, where u(x, t) = X(x)*T(t) > > You can view/pull and comment the code on: > http://github.com/plaes/sympy/tree/pde-separate > I don't know if you know about it, but the Maple PDEtools is documented in Cheb-Terrab, E.S. and von Bülow, K., "A computational approach for the analytical solving of partial differential equations", Computer Physics Communications 90, 1995, 102-116. It's available electronically and might give you some good ideas. It's about the original version so I don't know how different it is from the current version in Maple. > > A small example (or you can find some of them in the tests): > > from sympy import * > from sympy import Derivative as D > u, X, T = map(Function, 'uXT') > x, t = symbols('xt') > c = symbols('c', Real=True) > # Define our function (one-dimensional wave equation) > eq = Eq(D(u(x, t), t, 2), D(u(x, t), x, 2)*c**2) > print pde_separate_mul(eq, u(x, t), [X(x), T(t)]) > > out >> D(T(t), t, t)/T(t) == c**2*D(X(x), x, x)/X(x) > > > PS. Has anyone examples of equations that can be separated using > additive separation: u(x, t) = X(x) + T(t) > > There is some good information about separation of variables for PDEs in: Andrei D. Polyanin. "Handbook of Linear Partial Differential Equations for Engineers and Scientists". Chapman & Hall/CRC, Boca Raton, 2002. It has many PDEs and their solutions but also sections on how to approach solving them analytically. There is also a non-linear handbook. You can also find a fair bit of information at: http://eqworld.ipmnet.ru/ but not as much as are in the handbooks. Cheers, Tim. --- Tim Lahey PhD Candidate, Systems Design Engineering University of Waterloo http://www.linkedin.com/in/timlahey --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---
