[SciPy-user] first order pde

[Donald Fredkin]

Issa Karambal wrote:

> Hi all,
> 
> I am having  problem to solve numerically a hyperbolic equation like
> u_x=-pi*u_t, u(x,0)=exp(sin(x)), u(0,t)=u(2pi,t)=1. I used the method
> of lines; so I discretized the spatial domain using the centered
> finite difference method and thereafter I used the implicit Euler
> method, but I am still having problem after long time integration.
> If anyone has an idea on how I can solve numerically my problem?
> 
> THANKS,
> 
> issa

You can use the method of characteristics. The example you give is
easily solved numerically (and there is trouble with the boundary
condition at x = 2pi, as you might expect). If you must solve the
equation numerically, I'd suggest an upwind differencing method.

Don

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