1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding all solutions to non-linear system numericaly

  1. Sep 25, 2012 #1
    Hello world,

    Is it possible to find all solutions to a system of non-linear equations, without solving them analytically?

    I have implemented a python solution of Newton's Method, is there a method of getting good guesses without scanning all numbers?
  2. jcsd
  3. Sep 25, 2012 #2


    User Avatar
    Science Advisor

    What do you mean by "find all solutions"? You can, of course, approximate solutions. Is that what you mean by "finding" them? All numerical methods of solving equations will give one equation- typically, though not necessarily, the one closest to the chosen "starting value". So to find "all" solutions you would have to have some information about their possible values to begin with. And how would you know if you had found all solutions? What about equations that have an infinite number of solutions?
  4. Sep 25, 2012 #3
    By "find all solutions" I mean finding the roots. Is there a way to, numerically, analyse the functions. If I *don't* have any information about their possible values to begin with, find all possible roots.

    Hmm, I actually did no consider a system with infinite number of solutions. Hmm.

    So there is no way to find all roots, without doing a analytical analysis of the system?
  5. Sep 25, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    Correct. If you don't do some analysis, you don't even know how many roots there are.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook