What are solver best settings for my non linear equations?

Question

Javier 2019-9-3

0
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https://ww2.mathworks.cn/matlabcentral/answers/478653-what-are-solver-best-settings-for-my-non-linear-equations

Hello,

I have a set of non-linear equations that I would like to solve using fsolve, shown below in WandG function. Solver solutions are far away from the ones I would expect, I am expecting something alike x(1) = 10 and x(2)=0.11. Therefore, I would be glad if someone could give me some better directions of how to set up the options, especially tolerances, of the solver.

So far, I am reading this matlab documentation and I think that I may have to rewrite my equations with a better scaling but I am not sure whether or not this will be sufficient.

Thanks in advance

% configuration of fsolve    
    options = optimoptions('fsolve','Display','iter-detailed','PlotFcn',@optimplotfirstorderopt);
    options.StepTolerance = 1e-14;
    %options.OptimalityTolerance = 1e-14
    options.FunctionTolerance = 1e-14;
    options.MaxIterations = 100000;
    options.MaxFunctionEvaluations = 400;
    options.Algorithm = 'levenberg-marquardt';%'levenberg-marquardt';%'trust-region'%
    fun= @WandG;
    x0 = [5.0000e+00;5.5366e-03];
    % Solve the function fun
    gw =fsolve(fun,x0,options);
    % Function to be solved by fsolve
    function F = WandG(x)
        F(:,1) = ((((x(:,2)./10).*0.1).*(x(:,1)./100)).^2).*(8.9856e+01) +(( 7e-11 .* ( x(:,1)./100 ) ).^2).*( 1.7040e+08.^2.*(8.9856e+01) ) - (((x(:,2)./10).*0.1).*(x(:,1)./100)); 
        F(:,2) = ((((x(:,2)./10).*0.1).*(x(:,1)./100)).^2).*( 8.0640e+00 - 1.7040e+08.*1.1e-7 * (1-x(:,1)./200) ) + (((x(:,1)./100).*7e-11).^2).*( 1.7040e+08.^2*(8.0640e+00 - 1.7040e+08*1.1e-7 .* (1-x(:,1)./200)) ) + 1.7040e+08.*(7e-11.*(x(:,1)./100) );
    end