Solving set of nonlinear equations

Hi all,

I want to solve a set of non-linear equations (using fsolve), but the solver keeps giving errors. I am not much of a matlab user, but from what I've puzzled together I have written this in the editor, where I want to solve for x(1) and x(2):

    function F = dep(x)
  F = [log(1-(5.3e-3/2.1e-4))+x(1)-x(2)*(1-exp(-x(1)/x(2)));
      log(1+2*x(1)*(1-exp(-x(1)/x(2))))-x(1)+x(2)*(1-exp(-x(1)/x(2)))];
  end

I then define a range, and try to solve it, for example (I have played around with the numbers a bit):

x0=[1e-5 1e-1]
fsolve(@dep,x0)

, and I usually get an error referring to tolerances. I can't quite figure out what tolerances I should set, any help would be appreciated.

Many thanks!

Answer 1

[Matt J]

I don't get any errors, but I do end up with a complex-valued solution

        >>[x,fval]=fsolve(@dep,x0)

            x =

            -3.1889 - 3.2233i   0.4995 - 0.5068i

          fval =

             1.0e-04 *

             0.1903 + 0.1585i
            -0.0021 - 0.0014i

because your equations contain the complex valued quantity

      >> log(1-(5.3e-3/2.1e-4))

      ans =

         3.1879 + 3.1416i

I assume that that's a typo. The second equation also has a dangerous log expression that can become complex when the argument goes negative. It might be better to rewrite it as

       (1+2*x(1)*(1-exp(-x(1)/x(2))))-exp(x(1)+x(2)*(1-exp(-x(1)/x(2))))   =0