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MathGroup Archive 2009

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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


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