Solving a system of nonlinear equations containing integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg27166] Solving a system of nonlinear equations containing integrals*From*: anthozique at my-deja.com*Date*: Fri, 9 Feb 2001 03:10:15 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I would like to find roots for the following system of equations (my unknowns are a and b, Lambda and Sigma are just parameters): \!\(eq1\ = \ b\^2\ \[Lambda]\ Log[2] + 1\/6\ \((1 + Log[4])\) - \(1\/\[Sigma]\^2\) \((2\ a\^2\ *\ Integrate[\[ExponentialE]\^\(\(\(-r\^2\) - \ \[Rho]\^2\)\/\[Sigma]\^2\)\ r\ \[Rho]\ BesselI[ 0, \(2\ r\ \[Rho]\)\/\[Sigma]\^2]\ Sech[r\/b]\^2\ Sech[\ \[Rho]\/b]\^2, {r, 0, \[Infinity]}, {\[Rho], 0, \[Infinity]}])\)\) and \!\(eq2\ = \ \(-b\^2\)\ \[Lambda]\ Log[2] + 1\/\(b\ \[Sigma]\^2\)*\((2\ a\^2\ *\ Integrate[ r\^2\ *\[ExponentialE]\^\(\(\(-r\^2\) - \ \[Rho]\^2\)\/\[Sigma]\^2\)\ *\[Rho]\ * BesselI[0, \(2\ r\ \[Rho]\)\/\[Sigma]\^2]*\ Sech[\[Rho]\/b]\^2\ *Sech[r\/b]\^2\ *Tanh[r\/b], {r, 0, \[Infinity]}, {\[Rho], 0, \[Infinity]}])\)\) with e.g. Lambda=1 and Sigma=0.1 As you can see, this system contains some nasty equations involving integrals and bessel functions. I think I have tried nearly all kind of combinations of options that mathematica can offer, particularly combinations of FindRoot and NIntegrate, e.g. (with Lambda=1 and Sigma=0.1) FindRoot[{eq1,eq2},{a,2.16},{b,0.75},...] where eq1=....NIntegrate[]... and eq2=....NIntegrate[]...... I couldn't get any satisfactory result (without any warnings). Could anyone suggest me the best way to find roots for this system ? Sent via Deja.com http://www.deja.com/