Re: Does anybody?
- To: mathgroup at smc.vnet.net
- Subject: [mg49896] Re: Does anybody?
- From: Mike <m.HoneychurcNOSPAMh at uq.edu.au>
- Date: Thu, 5 Aug 2004 09:22:01 -0400 (EDT)
- Organization: University of Queensland
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
In electrochemistry the closed form solution for a technique called cyclic
voltammetry is a first kind volterra equation. If other reactions are
couples to the electrochemical reaction the solution is a 2nd kind volterra
or freidholm eqn. (I'm not a mathematician and always get the difference
between these mixed up).
I solve these in mathematica using a numerical method which seems to be the
convention in my field see:
Nicholson, R. S. and Shain, I. (1964). Analytical Chemistry, 36, 704-23.
Nicholson, R. S. (1965). Analytical Chemistry, 37, 1351-5.
Nicholson, R. S. and Olmstead, M. L. (1972). Numerical solution of integral
equations. In Electrochemistry; calculations, simulations, and
instrumentation, (ed. J. S. Mattson, H. B. Mark jnr., and H. C. MacDonald
jnr.), pp. 119-38. Marcel Dekker, New York.
Implementation in Mathematica depends on how much you know about
mathematica. A procedural implementation based on the methods described in
these refs is straight forward but slow. A functional implementation is a
bit more complicated but solves in less than a second (in my case the
problem must be solved at each potential and typically needs to be solved
400 or so times so less than a second per 400 results is good for me).
I seem to recall someone, (perhaps Paul Abbott?) writing an article on the
use of Chebyshev polynomials to solve integral equations. This was based on
an article in The computer journal in the 1960s. I only have incomplete
details of this article: S.E.El-gendi, page 282. I copied this article at
the time I read the mathematica article but unfortunately the copy doesn't
include the year and volume.
Hope that is of some help.
On 3/8/04 3:17 PM, in article cen755$bv$1 at smc.vnet.net, "Mithras"
<mithras at NOSPAM.blast.pl> wrote:
> Does anybody here met the problem of soving Integral equations. Maybe
> someone would give here link to some examples?
> Esspecialy of so called ill-posed problems (Fredholm equations of the FIRS
> kind) and Tchonov Reguralizations etc.
> Thank you very much for some help and hint!
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