```Date: Jun 15, 2012 3:34 PM
Author: Iván Lazaro
Subject: System of Integro-differential equations

Hi!I'm trying to solve a system of four integro-differential equationsusing Mathematica. I'm using Interpolation to do it, but until knowI'm not getting correct behaviors. Maybe the system is too complicatedto be solve like I'm trying, but maybe I'm making some silly mistake.For some reason the system is "exploding", but the first threevariables have to remain below 1 (in fact, their sum must remain below1).So, if anyone has some insight, it would be very welcome!It may look bad here because I'm using subscripts.Thanks in advance!n = 1;nf = 30;nEq = 4;Tau = 0.05;Table[If[i == 3, Subscript[c, i] = {1}, Subscript[c, i] = {0}], {i, 1, nEq}];Block[{\$RecursionLimit = \[Infinity]}, While[n < nf, Table[{     Table[Subscript[LC, i] = Table[{(j - 1) Tau, Subscript[c,i][[j]]}, {j, 1, n}], {i, 1, nEq}];     Table[Subscript[IntC, i] = Interpolation[Subscript[LC, i], If[i <4, Method -> "Spline", Method -> "Hermite"]], {i, 1, nEq}];     Which[k == 1, time = (n - 1) Tau, k == 2 || k == 3, time = Tau (n- 1/2), k == 4, time = Tau*n];     Subscript[c1, 1, k] = Tau*NIntegrate[0.1*(Subscript[IntC, 3][s] -Subscript[IntC, 1][s]) + 2.5*Subscript[IntC, 2][s], {s, 0, time},AccuracyGoal -> 10];     Subscript[c1, 2, k] = Tau*NIntegrate[-2.60*Subscript[IntC, 2][s]- 7*Im[Subscript[IntC, 4][s]], {s, 0, time}, AccuracyGoal -> 10];     Subscript[c1, 3, k] = Tau*NIntegrate[0.1 (Subscript[IntC, 1][s] -Subscript[IntC, 3][s]) + 7*Im[Subscript[IntC, 4][s]], {s, 0, time},AccuracyGoal -> 10];     Subscript[c1, 4, k] = Tau*NIntegrate[I*3.5*(Subscript[IntC, 2][s]- Subscript[IntC, 3][s]) - 1.35*Subscript[IntC, 4][s], {s, 0, time},AccuracyGoal -> 10];     Which[k == 1, Table[Subscript[c, i][[n]] = Subscript[c, i][[n]] +Subscript[c1, i, 1]/2, {i, 1, nEq}],      k == 2, Table[Subscript[c, i][[n]] = Subscript[c, i][[n]] +Subscript[c1, i, 2]/2, {i, 1, nEq}],      k == 3, Table[Subscript[c, i][[n]] = Subscript[c, i][[n]] +Subscript[c1, i, 3], {i, 1, nEq}],      k == 4, Table[Subscript[c, i][[n]] = Subscript[c, i][[n]], {i,1, nEq}]]}, {k, 1, 4}];   Table[Subscript[c, i] = Append[Subscript[c, i], Subscript[c,i][[n]] + (Subscript[c1, i, 1] + 2.0*Subscript[c1, i, 2] +2.0*Subscript[c1, i, 3] + Subscript[c1, i, 4])/6], {i, 1, nEq}]; n = n+ 1]];
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