Anyone have a "little" shooting-method function to share
David L Goldsmith
David.L.Goldsmith at noaa.gov
Thu Nov 9 15:02:33 CST 2006
Wow, thanks!
DG
Pauli Virtanen wrote:
> ke, 2006-11-08 kello 16:08 -0800, David L Goldsmith kirjoitti:
>
>> Hi! I tried to send this earlier: it made it into my sent mail folder,
>> but does not appear to have made it to the list.
>>
>> I need to numerically solve:
>> (1-t)x" + x' - x = f(t), x(0) = x0, x(1) = x1
>> I've been trying to use (because it's the approach I inherited) an
>> elementary finite-difference discretization, but unit tests have shown
>> that that approach isn't working.
>>
> [clip]
>
> You could try to use some of the pre-existing www.netlib.org codes for
> solving BVPs. This only requires writing a wrapper.
>
> However, I have written a wrapper for the COLNEW code, which is a
> finite-difference method written by Ascher & Bader in '87, having an
> adaptive mesh selection. You can find it here:
>
> http://www.iki.fi/pav/bvp
>
> As I understand, COLNEW does not have any special handling for singular
> coefficients, but nevertheless it seems to be able to solve your
> problem. The code goes as follows:
>
> ----------------------------------------------------
> import scipy as N
> import bvp
>
> u0 = 1
> u1 = 2
>
> def f(t):
> return N.sin(2*t)
>
> def fsub(t, z):
> u, du = z
> return N.array([(f(t) + u - du)/(1-t)])
>
> def gsub(z):
> u, du = z
> return N.array([u[0] - u0, u[1] - u1])
>
> tol = [1e-5, 1e-5]
> boundary_points = [0, 1]
>
> solution = bvp.colnew.solve(boundary_points, [2], fsub, gsub,
> is_linear=True, tolerances=tol,
> vectorized=True, maximum_mesh_size=300)
>
> import pylab
>
> x = solution.mesh
> pylab.plot(x, solution(x)[:,0])
> pylab.savefig('solution.png')
> ----------------------------------------------------
>
> BR,
>
> Pauli Virtanen
>
>
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>
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