Mathematica Asked on May 6, 2021
Here is the code by P. Valko and J. Abate for finding numerical inverse Laplace transform by trapezoidal’s rule. Can someone willing to explain this code? I don’t understand this part: Plus @@ Append
talbot[F_, t_, M_: 32] :=
Module[{np, r, S, theta, sigma},
np = Max[M, $MachinePrecision];
r = SetPrecision[2 M/(5 t), np];
S = r theta (Cot[theta] + I);
sigma = theta + (theta Cot[theta] - 1) Cot[theta];
(r/M) Plus @@ Append[Table[Re[Exp[t S] (1 + I sigma) F[S]],
{theta, Pi/M, (M - 1) Pi/M, Pi/M}],
(1/2) Exp[r t] F[r]]]
fun[s_] = 1/(s - 1); %example use
t0 = 1;
ft = talbot[fun, t0]
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