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Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.

3
votes
T[f_] := t + Integrate[f /. t -> s, {s, 0, t}]; NestList[T, t, 5] (* Out: {t, t + t^2/2, t + t^2/2 + t^3/6, t + t^2/2 + t^3/6 + t^4/24, t + t^2/2 + t^3/6 + t^4/24 + t^5/120, t + t^2/2 …
answered Jul 22 '14 by Mark McClure
2
votes
The iteration can be performed as follows: A[t_] = {{t, 0}, {Cos[t], 1}}; B[t_] = {{Exp[t], 0}, {0, Exp[-t]}}; T[F_] := Expand[A[t] + Integrate[B[s].F /. t -> s, {s, 0, t}]]; iteration = NestList[T, …
answered Jul 24 '14 by Mark McClure
4
votes
You are almost certainly going to need to evaluate test numerically, so let's just use NIntegrate from the start. Clear[e, a, p, s, t] e[t_] := (E^(-t^2)) Cos[0.1 t]; a[t_?NumericQ] := NIntegrate[e[x …
answered Dec 23 '14 by Mark McClure