| Fredholm integral equation [message #88888] |
Tue, 01 July 2014 10:52  |
Gompie
Messages: 76
Registered: August 2012
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Dear All,
I wish to solve a Fredholm integral equation of the first kind. Is there an idl routine that can do this.
My Equation is of the kind
knownfunction = integral( knownfunction X unknownfunction)
-GlanPlon
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| Re: Fredholm integral equation [message #88917 is a reply to message #88907] |
Thu, 03 July 2014 09:18  |
Bill Nel
Messages: 31
Registered: October 2010
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On Wednesday, July 2, 2014 2:54:07 PM UTC-4, Gompie wrote:
> Thanks once again for the suggestion. I guess the following thing should work.
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> Trapezoidal rule can be written as
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> 0.5*[(x2-x1)f(x1) + (x3-x1)*f(x2) + (x4-x2)*f(x3) +...].
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> Here f(x)=knownfunction*unknownfunction.
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> The above expression is a ## multiplication of two vectors hence is respresentable as a expression you mentioned in your message (i.e knownVector = knownMatrix ## unknownVector)
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> -GlanPlon
I may be misunderstanding your problem, but what I meant was that if you have
h(x) = Integral_dy{ f(x,y) g(y) }
this can be approximated as
h(i dx) = (1/dy) Sum_over_j{ f(i dx, j dy) g(j dy) }
where i = 0, 1, ...
j = 0, 1, ...
and dx, dy are your (equal) grid spacing. This is just a matrix equation
h[i] = (1/dy) f[i, j] g[j]
with h and f known, g unknown.
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