I review this question Solving a Volterra integral equation numerically. But I can not understand that. I have the following code:
u[1][x_] = (-k)*(E^(Pi*x) + x);
u[2][x_] = Refine[Integrate[(x - t)*E^u[1][t], {t, 0, x}], E^(Pi*x) >= 0]
K is constant. Any suggestions analytical or numerical?
u[x] == Integrate[(x - t)*E^u[t], {t, 0, x}]? Whatever it is, it should be given explicitly in the question. – Daniel Lichtblau Jun 26 '17 at 14:43