[SciPy-User] odeint

[Charles R Harris]

On Sun, Aug 12, 2012 at 1:49 PM, nicky van foreest <vanforeest at gmail.com>wrote:

> Hi Rob,
>
> Thanks for the suggestion. I didn't think of using splines.
>
> Nicky
>
> On 10 August 2012 10:09, Rob Clewley <rob.clewley at gmail.com> wrote:
> > Hi,
> >
> > On Thu, Aug 9, 2012 at 2:15 PM, nicky van foreest <vanforeest at gmail.com>
> wrote:
> >> I am using odeint to integrate the following delay differential equation
> >>
> >> df/dx = c + f(x) - f(x-1)
> >>
> >> somewhat cumbersome. Is it possible in odeint to somehow get
> >> intermediate values of the function values?
> >
> > Nicky, I think your easiest way ahead here is to use a spline to fit
> > your previous intervals' solution function, building up your solution
> > using one that meets values and first derivatives at the end points to
> > retain smoothness as you go. Scipy offers several such spline tools.
> > Then you can sample that to your heart's content.
> >
> > --
> > Robert Clewley, Ph.D.
> > Assistant Professor
> > Neuroscience Institute and
> > Department of Mathematics and Statistics
> > Georgia State University
> > PO Box 5030
> > Atlanta, GA 30302, USA
>

Depending on the time interval, it might work to treat the equation as a
Chebyshev series by using its values at the Chebyshev points. Both the
derivative and the delay are then linear operators that can be represented
by matrices, see Trefethen's
book<http://people.maths.ox.ac.uk/trefethen/spectral.html>for the
differentiation matrices. The boundary conditions might be a bit
tricky, but you don't mention how you handle the delay there.

Chuck
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