Inversion algorithm for Laplace Domain

Skin = 1;
ET = 0.3;
φ = 0.1;
ω = 10^-6;
τ = 0;
Cd = 100;

PD[s_] = (BesselK[0, Sqrt[s]] + Sqrt[s] BesselK[1, Sqrt[s]]
{Skin - (ET φ I ω Exp[s I ω τ])/(s - I ω)})/(Cd s^2 (BesselK[0, Sqrt[s]] +
Skin Sqrt[s] BesselK[1, Sqrt[s]]) + s Sqrt[s] BesselK[1, Sqrt[s]]);

tmax = 25000000;
T = 4*tmax;
e = 10^-8;
a = -(Log[e]/(2 T));

ad[tmax_, alpha_, tol_] := ad[tmax, alpha, tol] =
alpha - Log[tol]/(8 tmax) // N

cd[PD_, s_, tmax_, alpha_, tol, k_] := PD /. s -> ad[tmax, alpha, tol] +
I Pi k/(4 tmax) // N

sd[F_, s_, t_, j_, tmax_, alpha_: 0, tol_: 0.00000001] :=
Inv[PD, s, t, j, tmax, alpha, tol] =
Exp[ad[tmax, alpha, tol] t]/(4 tmax) * Sum[Re[cd[PD, s, tmax, alpha, tol, k]]
Cos[k Pi t/(4 tmax)] - Im[cd[PD, s, tmax, alpha, tol, k]] Sin[k Pi t/(4 tmax)],
{k, 0, j}] // N

LogLogPlot[{PD[y], y*PD'[y]}, {y, 10, 1000000000},
PlotRange -> {0.01, 100}, PlotStyle -> {{Black}, {Dashed, Blue}},
Frame -> True, FrameLabel -> {"tD", "PD e tD*PD'"},
BaseStyle -> {FontSize -> 12}]


I'm trying to invert an equation in the Laplace domain using Stehfest algorithm. It works very fine, but since I'm trying to represent a sinusoidal behaviour I need a different algorithm that makes use of the Fourier Series. Does anyone have experience in programming such algorithms? Here, I'm trying to use Durbin-Crump Method, but no success so far...

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Please, include a working example /code snippet/, so the users may actually contribute :) – Sektor Aug 22 '13 at 13:49
Why do you put [] around names of your variables? like this [CurlyPhi] = 0.1; [Omega] = 10^-6 did you read that somewhere in the documentation? ALso it is bad idea to use UpperCaseFirstLetterForYourVariablesAndSymbols since this can conflict with Mathematca's own and also can be confusing to the reader. lowerCaseFirstLetterWillWorkJustAsWell` – Nasser Dec 9 '13 at 14:12
Nasser, since it worked fine with Sthefest Algorith I assumed it would work as well for the Durbin-Crump Algorithm... I dindt see a reason for an error... – Bruno Rangel Dec 9 '13 at 14:58
Sthefest algorithm has problems with trigonometric and exponential functions, you con use the Peter Valko program in mathematica. You can find de program on line on Peter Valko's web of Texas A&M University – Francisco Castellanos Jul 7 at 12:13