1. Not finding help here? Sign up for a free 30min 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!

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

  1. Feb 15, 2007 #1
    Question

    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

    berkeman

    User Avatar

    Staff: Mentor

    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.
     
  4. Feb 16, 2007 #3
  5. Feb 16, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: PLS, some one help me find the 1st 4 iterates using Picard's iteration.
  1. Picard Iteration (Replies: 0)

  2. Picard Iteration (Replies: 4)

Loading...