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Existential Proof of a Unique Solution to a Set of Non-Linear Equations

  1. Oct 27, 2008 #1
    Dear all,

    I have a set of 5 non-linear equations with highly complicated and long forms for which I wish to find the unique solution. I was going to tackle this problem with Broyden's method since the derivatives cannot be easily found.

    However, even if I get a solution from this, this is not the same as proofing that only one unique solution exists.

    What method would readers recommend I employ to attempt to prove whether there is a unique solution or not to this problem? I was thinking along the lines of covariance matrices...

  2. jcsd
  3. Oct 28, 2008 #2
    Assume that two distinct solutions exist, then derive a contradiction.
    It's difficult to say further without more information about your problem.
  4. Oct 18, 2010 #3
    Have you tried assuming that there are two solutions (just label as s_1 and s_2). Then apply them through the equations and find a contradiction to the assumption.
  5. Oct 18, 2010 #4
    What makes you think that the solution is (should be) unique, to start with?
    A set of nonlinear algebraic equations (it seems to me you are not talking about differential equations) can have more than one solution.
    For example, a set of two quadratic equations with two unknowns can have two distinct solutions.
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