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PLS, some one help me find the 1st 4 iterates using Picard's iteration.

  1. Feb 15, 2007 #1

    Use Picard's iteration to find the first 4 iterates of solutions of the problem dx/dt = -tx, x(0) = 1.

    If any one can help me solve this, I'll be so grateful. I wait anxiously to get the solution.
  2. jcsd
  3. Feb 16, 2007 #2


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  4. Feb 16, 2007 #3
    Last edited by a moderator: Apr 22, 2017
  5. Feb 16, 2007 #4


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    If you have the differential equation dx/dt= f(x,t) with x(t0)= x0 then "Picard's interation", used in his proof of the existance of solutions of the initial value problem, is
    [tex]x(t)= \int_{t_0}^t f(x,t)dt+ x_0[/tex]
    starting with x(t)= x0 and then using the resulting x(t) in the next iteration.

    Here, f(x,t)= -tx and x(0)= x0= 1 so the first "iteration" is
    [tex]\int_0^t -tdt+ 1[/itex]
    Surely you can continue from there.
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