Solving integral equations numerically

*To*: mathgroup at smc.vnet.net*Subject*: [mg99982] Solving integral equations numerically*From*: viehhaus <g.viehhauser1 at physics.ox.ac.uk>*Date*: Thu, 21 May 2009 00:05:08 -0400 (EDT)

Hi, I'm trying to solve a set of two integral equations, which don't have an analytic solution, so I'm using NIntegrate and FindRoot nodes = 11 (*number of nodes*) RCOM = 2.17 (* common resistance *) RS0 = 0.1 (*off-sensor resistance for sensor*) RS = 1.1 (*sensor resistance pre node*) Ph = 6 (*hybrid power in W*) tcool = -25 (*coolant temperature (degC) *) ta = 1.2/2/0.0000862 (*activation temperature (K) *) l = 63.56/1000(*length of thermal path*) w = 128.05/1000(*width of thermal path*) T0 = 273 + tcool + Ph*RCOM T = 4/3*(Tlo - T0^2/ta)*(x^2/l^2 - 2*x/l) + Tlo (*parabolic temperature function in sensor*) I1 = (RCOM + RS0)*w*qref*Exp[ta/273]/273^2*NIntegrate[T^2*Exp[-ta/T], {x, 0, l}] I2 = (RS/l)*w*qref*Exp[ta/273]/273^2*NIntegrate[T^2*Exp[-ta/T]*x, {x, 0, l/2}] FindRoot[{Tlo == T0 + I1, T0^2/ta == Tlo + I2}, {{Tlo, 270}, {qref, 300}}] but I get errors like "... has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,0.06356}}..." and FindRoot does not move. Any idea what I'm doing wrong? Cheers, Georg

**Follow-Ups**:**Re: Solving integral equations numerically***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: Solving integral equations numerically***From:*DrMajorBob <btreat1@austin.rr.com>