# Solving a system of integral equations by iteration with NestList

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 Sergi Gonzalez-Solis 1 Vote Hi all,I have to solve the following system of equations.F1[s_]=NIntegrate[F1[sp]*T1[sp]/(sp-s-I*10^-6),{sp,0.6,Infinity}]+NIntegrate[F2[sp]*T2[sp]/(sp-s-I*10^-6),{sp,1.1,Infinity}];F2[s_]=NIntegrate[F1[sp]*T2[sp]/(sp-s-I*10^-6),{sp,0.6,Infinity}]+NIntegrate[F2[sp]*T1[sp]/(sp-s-I*10^-6),{sp,1.1,Infinity}];I have to solve it iteratively, that is, I should give an initial function for both F1 and F2 (the so-called F1input, F2input below), and resulting F1 and F2 functions are calculated. Then, I should make use of these new functions and do the same as before. The procedure should be iterated until after n steps the procedure converges. Notice that the integrals also depends on s, which is a variable that in my case runs from 0 to 3.I tried the following to get my problem solved but it does not works as desired unfortunately.data = Table[{s, NestList[Apply[Function[{F1,F2}, {Abs[NIntegrate[F1*T1[sp]/(sp-s^2-I*10^-6),{sp, 0.6, Infinity},PrecisionGoal->1,MaxRecursion->100]+NIntegrate[F2*T2[sp]/(sp-s^2-I*10^-6),{sp, 1.1, Infinity},PrecisionGoal -> 1, MaxRecursion -> 100]],Abs[NIntegrate[F1*T2[sp]/(sp-s^2-I*10^-6),{sp, 0.6, Infinity},PrecisionGoal->1,MaxRecursion -> 100]+NIntegrate[F2*T1[sp]/(sp-s^2-I*10^-6),{sp,1.1, Infinity},PrecisionGoal -> 1,MaxRecursion -> 100]]}], #] &,{F1input[sp],F2input[sp]}, 1]},{s, 0, 3, 0.25}]To sum up I want to obtain a table giving me three entries: F1 and F2 for each value of s analyzed.Your help would be really appreciated. Thank you so much in advance. Sergi
5 years ago
4 Replies
 Todd Rowland 1 Vote Just on a cursory inspection, not sure your equations were written down correctly because they are identical so F1==F2.Your stated goal of getting three approximate solutions means you would want Nest instead of NestList (which gives all the intermediate approximations as well).Not sure why there is an Abs in there.The way you have setup your function, F1 and F2 are supposed to be values, approximations to F1, F2, so the initial conditions should be guesses too, and of course you might want to run the iteration for more than 1 step (the third argument of NestList) and finally one need not expect that the iteration will actually solve the Integral equations.