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Technique on solving non-linear ODE

  1. May 21, 2007 #1
    I have a set of non-linear ODE.
    There are eight variables that depends on time (t)
    4 of those are first order ODE
    1 of those are first order non-linear ODE
    3 of those are non-linear equations

    The variables are
    (t)

    (p)
    (ps)
    (gs)
    (gd)
    (as)
    (ad)
    (hs)
    (cs)

    k1,k2,k3,k4,k5 are constants

    The following initial condition are given at t=0
    (p)
    (gs)
    (gd)
    (as)
    (ad)


    The diff equations are

    note: f(t) is a set a data defined from t =0 from t=1000

    #1: d(p)/d(t) = (ps)-(p) + f(t)

    #2: d(gs)/d(t) = (gd)-(gs)-(ps)-(p)-k3

    #3: d(gd)/d(t) = (gd) - (gs)-k1

    #4: d(gd)/d(t) =(gd)-(gs) -k2

    #5: d(gd)/d(t) = (gd)-(gs)-k4


    The non-linear equations are

    #6: (ps) = ((hs)^2)/(cs)

    #7: (cs) = ((as)-(hs))/2

    #8: (hs) = (gs) - {(gs)^2 - k5*(as)*[2*(gs)-(as)]}^(1/2)

    I figure there are two approaches so far

    1st approach:)
    I figure I can figure differentiate #6, #7, #8 and figure out their initial condition and use ODE45 or ODE23 to solve this system

    However, #8 will be very messy......

    2nd approach:)
    I can solve for (ps) using #6, #7 and #8 and thus I have a system of
    5 non-linear ODE. (#1 - #5) It is still very messy......


    Any ideas in this kind of situation???

    Also, what do I need to do for f(t) as it is given as a set of points and not a well-defined function.

    Thanks so much for your help
     
  2. jcsd
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