[SciPy-user] Relatively simple PDE's and Scipy

Sebastian Walter sebastian.walter@gmail....
Wed Apr 22 04:58:25 CDT 2009


I'm not sure I understand correctly: but if you want a quick way to
solve such problems you can use the "method of lines":
I.e. discretize either the time t or the space x and then apply an ODE
solver available in scipy:

e.g. the above equation leads to a system of ODEs
\partial_t f(x_n,t) + [g(x_{n+1})  - g(x_n})]/h = 0      n=0,...,N_gridsize

where h = x_{n+1} - x_n
and g = f(t,x)/x





On Wed, Apr 22, 2009 at 11:39 AM, Lorenzo Isella
<lorenzo.isella@gmail.com> wrote:
> Dear All,
> I hope this is not too off-topic.
> Some time ago I posted about the general availability of PDE solvers
> under SciPy.
> Now I can be more specific; say you are given the equation
>
> \partial_t f(x,t)+\partial_x(f(x,t)/x)=0,
> where t is time and x is position in 1D. I would say that I am dealing
> with a 1D PDE (so, nothing like solving a multi-dimensional PDE on a
> complex domain).
>
> Do you think there is any ready-to-use method to tackle this kind of
> equation under (or tightly integrated with) SciPy?
> I stress that x is a scalar variable and not a vector. Overall, it
> does not look (naively) a terrible equation, but I am having a hard
> time with it.
> Many thanks
>
> Lorenzo
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