[SciPy-user] Linear Integral Equation second kind
Bobo South Africa
wizzard028wise@gmail....
Tue Apr 3 17:48:14 CDT 2007
Hi Anne,
You have sent to me exactly what I was looking for.
Thanks you !
2007/4/3, Anne Archibald <peridot.faceted@gmail.com>:
>
> On 03/04/07, Bobo South Africa <wizzard028wise@gmail.com> wrote:
> > Hi all,
> >
> > I would want to compute the numerical solution of the following integral
> > equation
> > ( Volterra integral equation for the second kind) :
> >
> >
> >
> > f(t) = \int_{a}^{ b} f(t-x)g(x)dx + h(t) (latex
> > symbol)
> >
> > where the unknown function is f(t).
>
> As far as I know, scipy does not implement solving these equations.
> But it does implement some tools which should allow you to solve them
> quite efficiently (at least in terms of your time, possibly not in
> terms of CPU time).
>
> I recommend looking at Numerical Recipes:
> http://www.nrbook.com/b/bookcpdf.php
>
> See if the algorithms they describe can take advantage of the tools in
> scipy - in particular, there are both smart adaptive quadrature rules
> and splines, if you'd like to work with a spline representation of
> your function. Alternatively, if you want to compute your function on
> a grid and use numerical integration adapted to the grid, scipy
> implements not only trapezoidal and Simpson integration on arbitrary
> grids, in scipy.special you will find various families of orthogonal
> polynomials along with all the coefficients to do Gaussian integration
> in terms of those. Finally, even if you implement the calculation
> mostly by hand, be aware that there are a host of linear algebra tools
> to help.
>
> Anne
>
>
>
>
> >
> > Thank for your help
> >
> >
> >
> >
> >
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> >
> >
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