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Re: Radially symmetric point source diffusion with decay
Posted:
Apr 26, 2012 9:22 AM
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Gib Bogle <g.bogle@auckland.ac.nz> writes:
> Sorry Peter, I meant to say that it's the steady state solution that I
> want. I know that for the decay rates of interest the concentration
> is very close to zero at r_end = 30, and for my purposes I don't care
> about the tiny difference between the solutions for r_end = 20 and
> r_end = 30. As it turns out the shooting method with Newton-Raphson
> works very well, and is quite robust with a wide range of starting
> slope. From a bit of reading I can see that there probably will not
> be a tractable analytical solution - even Laplace's eqtn for the 3D
> case has a rather complicated series solution involving positive and
> negative powers of r.
Maybe I don't understand your problem correctly, but the
radially-symmetric Laplace solution with bc 0 at infinity should be the
standard 1/r-potential (multiplied by some factor to fit the value at
r=1).
Nicolas
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