Problems in Nintegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg121360] Problems in Nintegrate
• From: Jiwan Kim <hwoarang.kim at gmail.com>
• Date: Mon, 12 Sep 2011 04:21:38 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hello, Mathgroup.

By solving the coupled differential equation, I got Te[z,t] and Tl[z,t]
solution in the following code.
Then, I wanted to get the Eta[z,t] using NIntegrate function.
I am using the ver. 7.0 and AMD dual core, 2GB memory.
I confirmed that the my code below is working for higher version or a better
computer.
But it is not working with my computer and program ver.
I have no idea for these errors...
The representative error messages are like followings:

* Solve::ifun: Inverse functions are being used by Solve, so some solutions
may not be found; use Reduce for complete solution information. >>
* NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy
after 9 recursive bisections in t2 near {t2} = {-0.69605}. NIntegrate
obtained -8.17582 and 0.0012150431662771995` for the integral and error
estimates. >>

Is there anything wrong? could you help me ?

Jiwan.
_________________________________________________________
Remove["Global`*"];
\[Rho] = 8910;(* mass density : kg/m^3 *)
v = 4.08;(* sound velocity : nm/ps *)
\[Beta] = 1.3 10^-5;(* linear expansion : /K *)
B = 1.8 10^11; (* bulk modulus : Pa *)
c = 3 10^5; (* light speed : nm/ps *)
\[Lambda] = 800; \[Omega] =
2 \[Pi] c/\[Lambda]; (* light wavelength : nm *)
Ce = 1.065 10^3; (* electron heat cap. at 300 K : 3.19 10^5 J/m^3K *)
Cl = 3.95 10^6; (* lattice heat cap. : J/m^3K = 26.1 J/mol.K *)
g = 4.4 10^5; (* coupling constant : 4.4 10^17 W/m^3.K *)
K = 91 10^6; (* thermal conductivity : 91 W/m.K -> 91 10^18 *)
\[Xi]1 = 13.5; (* pump absorption depth: nm *)
\[Xi]2 = 14.5; (* probe absorption depth: nm *)
Dl = 2.3 10^-5; (* diffusivity : m^2/s *)
R = 0.4; (* reflection at interface *)
I0 = 1.05 10^10; (* 2.77 10^13 J/m^2.pulse(ps) -> 2.77 10^22 *)
PulseWidth = 0.2 ; (* 200 fs *)
S[t_] := I0 Exp[-t^2/(2 PulseWidth)^2];
pow[z_, t_] := 1/\[Xi]1 S[t] Exp[-z/\[Xi]1]; (* W/m^3 *)
L = 1000; (* sample thickness : nm *)
solution =
NDSolve[{Ce Te[z, t] D[Te[z, t], t] ==
K D[Te[z, t], z, z] - g (Te[z, t] - Tl[z, t]) + pow[z, t],
Cl D[Tl[z, t], t] == g (Te[z, t] - Tl[z, t]),
Te[z, -100] == Tl[z, -100] == 300,
Te[L, t] == 300, (D[Te[z, t], z] /. z -> 0) == 0}, {Te, Tl}, {z,
0, L}, {t, -100, 100}, MaxSteps -> Infinity,
MaxStepSize -> {1, 0.1}][[1]]
solz = {Te[z, t], Tl[z, t]} /. solution /. z -> 0;
Plot[solz /. t -> tau, {tau, -2, 100}, PlotRange -> All]
dTl = (D[Tl[z, t] /. solution, t] /. {z -> Abs[zz - v (t1 - t2)],
t -> t2});
\[Eta][z_,
t_] := -((3 B \[Beta])/(2 \[Rho] v^2)) NIntegrate[
Evaluate[
Sign[zz - v (t1 - t2)] dTl /. {zz -> z, t1 -> t}], {t2, -100,
100}, AccuracyGoal -> 4, Exclusions -> {t2 == 0}];
vals = Table[{t, \[Eta][1, t]}, {t, 1, 20, 0.5}]
ListPlot[vals]
------------------------------------------------------------------------------

-----------------------------------------------------------------------------
Institute of Physics and Chemistry of Materials Strasbourg (IPCMS)
Department of Ultrafast Optics and Nanophotonics (DON)
23 rue du Loess, B.P. 43,
67034 STRASBOURG Cedex 2, France

```

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