       coupled integral equations

• To: mathgroup at smc.vnet.net
• Subject: [mg21062] coupled integral equations
• From: francesco siano <fsiano at usc.edu>
• Date: Sun, 12 Dec 1999 23:51:26 -0500 (EST)
• Organization: USC-Physics
• Sender: owner-wri-mathgroup at wolfram.com

```Hi, I'd appreciate any help on this problem.
I have to solve a system of integral equations of the form :
eps1[x]=c1*eps0[x]+Integrate[kernel[x-y]*f[eps3[y]],{y,a,b}]
eps2[x]=c2*eps0[x]+Integrate[kernel[x-y]*f[eps3[y]],{y,a,b}]
eps3[x]=c3*eps0[x]+Integrate[kernel[x-y]*(f[eps1[y]]+f[eps2[y]]),{y,a,b}]

eps4[x]=c4*eps0[x]+Integrate[kernel[x-y]*f[eps3[y]],{y,a,b}]
(where the functions kernel, f, and the constants c1,c2,c3,c4,a,b, are
all known) for x in the same interval [a,b].
All I can think of is to consider [a,b] as a grid of discrete values,
and calculate each function iteratively starting from the known
zero-order value ci*eps0[x] (evaluating the integrals with
ListIntegrate). This works, but very slowly. I couldn't figure out any
smart solution. Thanks for any hint.
-Francesco Siano
USC

```

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