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

  • Thread starter manttiz
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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.
 

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  • #2
berkeman
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Welcome to the PF. We do not provide solutions to your homework. You must show us the relevant equations and concepts that apply to your question, and you must show us your work so far so that we can provide some tutorial help. In the future, please completely fill out the Homework Posting Template that is provided to you when you start a new Homework Help thread.
 
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HallsofIvy
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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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