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*: <cen755$bv$1@smc.vnet.net>*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. Cheers Mike 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! > Mithras > >