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Solution of non-linear set of equations

  1. Aug 6, 2009 #1
    Hi

    Consider a set of n non-linear equations and I have m unknowns and n<m, so I don't have enough equations to solve the problem. All the unknowns are parametrized by say t

    A possible solution to this that I considered was to take the derivative w.r.t. t and obtain another set of n equations, if 2n > m then I have more equations than unknowns and I these can be solved.

    Now will this work?

    cheers

    M
     
    Last edited: Aug 6, 2009
  2. jcsd
  3. Aug 6, 2009 #2

    Dick

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    If you consider the derivatives as well, you get 2n equation is 2m unknowns. Since the derivatives are unknown as well.
     
  4. Aug 6, 2009 #3
    Sorry I was not clear the equations are really differential equations but I dont want a solution for all t just for 1 so i'm treating each derivative as an unknown. So I have
    [tex]f_i(x_i(t),x_i'(t),x_i''(t)...) = 0[/tex] it is possible to have 2n>m+1, if not I just take extra derivatives until it is. Will this work or have I 'cheated'?


    cheers

    M
     
  5. Aug 6, 2009 #4

    Dick

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    Maybe if you more specific in the problem you are actually trying solve we could help more. But you can't magically solve an under-determined system by taking derivatives.
     
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