Re: Help to solve a large system of Nonlinear equations

Nicolas Charest wrote:
> 
> I tried to solve a system of 41 nonlinear equation - 41 variables.
> Physically,This system describe a very hyperstatically concrete girder
> behavior under large loads.
> 
> The system is:
> 
> 41 variables:
> P,M0,M1,M2,M3,M4,Vba,Vca,Vda,Vea,f1p,f2p,f3p,f4p,K1,K3,K4,K5,K6,K7,K8,Lam1,Lam2,
> Lam3,Lam4,f1c,f2c,f3c,f4c,c1,c2,c3,c4,T1x,T2x,T3x,T4x,Tde,Tcd,Tbc,Tab
> 
> 41 equations:
> "-M0+L*P/4-L/8*tan(f4c)*T4x-L/8*tan(f3c)*(T3x+T4x)-L/8*tan(f2c)*(T2x+T3x+T4x)-L/8*tan(f1c)*(T1x+T2x+T3x+T4x)+T4x*Vea+T3x*(Vea-Vba)+T2x*(Vea-Vca)+T1x*(Vea-Vda)-T4x*e-T3x*e-T2x*e-T1x*e=0"
>

Levenberg-Marquardt "lmdif" from http://netlib.org should do it. It
generates the Jacobian numerically and will let you, with some minor
editing, quickly reuse the work you've already done. i.e. in the fcn
describing the system,

        -- define P = x(1); ... Tab = x(41)
        -- replace all "... = 0" with "f(i) = ..."

Incidentally, "lmdif" is in the "minpack" library.

--
Dr.B.Voh
------------------------------------------------------
Applied Algorithms    http://sdynamix.com