solve a PDE with pdsolve

[rolfd...@gmail.com]

Hi,
I have just started using sympy and tried to solve a PDE like this:





My approach in sympy was:

from sympy.solvers.pde import pdsolve
from sympy import Function, diff, pprint, Eq, init_printing
from sympy.abc import x,t,c
init_printing()
u = Function('u')
w = Eq(diff(u(t),t,2) - (c**2*diff(u(x),x,2)),0)
pdsolve(w, u(x,t),hint="all")

Unfortunataly I've got some error-messages which I can't handle.
Is there any help?
Thanks a lot.


The error messages were:

ValueError                                Traceback (most recent call last)
<ipython-input-12-e0eef578ab5a> in <module>()
----> 1 pdsolve(w, u(x,t),hint="all")

C:\WinPython\WinPython-32bit-3.5.2.1\python-3.5.2\lib\site-packages\sympy\solvers\pde.py in pdsolve(eq, func, hint, dict, solvefun, **kwargs)
    171     # See the docstring of _desolve for more details.
    172     hints = _desolve(eq, func=func,
--> 173         hint=hint, simplify=True, type='pde', **kwargs)
    174     eq = hints.pop('eq', False)
    175     all_ = hints.pop('all', False)

C:\WinPython\WinPython-32bit-3.5.2.1\python-3.5.2\lib\site-packages\sympy\solvers\deutils.py in _desolve(eq, func, hint, ics, simplify, **kwargs)
    224     if hints['order'] == 0:
    225         raise ValueError(
--> 226             str(eq) + " is not a differential equation in " + str(func))
    227 
    228     if not hints['default']:

ValueError: -c**2*Derivative(u(x), x, x) + Derivative(u(t), t, t) is not a differential equation in u(x, t)

−c2d2dx2u(x)+d2dt2u(t)=0




M

[Aaron Meurer]

You need to use u(x, t) everywhere. SymPy considers u(x) and u(x, t) to be completely different functions. 

Unfortunately, pdsolve is currently not very powerful, and it is unable to solve your PDE.

Aaron Meurer

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[rolfd...@gmail.com]

Pity, it is a very important PDE, it is the one-dimensional wave equation. Nevertheless many thanks.

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