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 ? Thank you in advance. 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