title: How to solve simultaneous non-linear equations with exponential functions?
body: <p>I have a system of equations to solve for <code>x1</code> and <code>x2</code>: </p>
  
  <pre><code>2*erf(A*x2)*exp(B*x1^2+C*x2^2)-D*erf(x1)=0
  
  2*erf(D*x2)*exp(E*x1^2+F*x2^2)-G*erf(x1)-erf(H*x2)*exp(I*x1^2)=0
  </code></pre>
  
  <p>where <code>B</code> and <code>C</code> are negative while rest of the constants are positive.</p>
  
  <p>I tried to solve it in C using multiroot function from the GSL library. It seems that multiroot was not able to solve the system. I tried the same implementation of multiroot for non-linear simultaneous polynomial functions (no exponential part in it) and it worked well and gave correct results. 
  Any suggestions on how to solve such a system? Or any other powerful library which can be used for such equations?</p>