NIntegrate and FindRoot error

*To*: mathgroup at smc.vnet.net*Subject*: [mg75639] NIntegrate and FindRoot error*From*: "Judith Bunder" <bunder at phys.cts.nthu.edu.tw>*Date*: Mon, 7 May 2007 05:36:53 -0400 (EDT)*References*: <20070507050017.M68851@phys.cts.nthu.edu.tw> <463EC1B7.1080102@smc.vnet.net>

Hi, I have to perform a double integral. To evaluate the integrand I have to use FindRoot and this seems to work as I can evaluate the integrand at specific points and even make a 3D plot over the whole range. However, when I try to use NIntegrate I get a FindRoot::"nlnum" error message: Here is a simplified version of my code: Ly = 3; w = 5; t2 = 1; t1[kx_] := 2 t2 Cos[kx/2]; py[kx_, m_ /; m >= 1 && m <= Ly] := p/. FindRoot[(2 Ly + 1) p +ArcTan[ Tan [p] (t1[kx] - t2)/(t1[kx] + t2)]==m Pi,{p,1}] WG[kx1_, kx2_] := Sum[Sum[py[kx1, m1] py[kx2, m2],{m1,1,Ly-1}],{m2,1,Ly-1}] Plot3D[Re[Exp[ I w (a2 - a1)] WG[a1, a2]], {a2, -Pi, Pi}, {a1, -Pi, Pi}] Plot3D[Im[Exp[ I w (a2 - a1)] WG[a1, a2]], {a2, -Pi, Pi}, {a1, -Pi, Pi}] NIntegrate[Exp[ I w (a2 - a1)] WG[a1, a2], {a2, -Pi, Pi}, {a1, -Pi, Pi}] The NIntegrate command fails. It appears to be objecting to my Cos[2 kx] function in the FindRoot command. I don't understand why it would object as Plot3D over the same integrand worked. Thanks a lot, Judy Bunder