1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Euler's Method - Global Error

  1. Nov 24, 2011 #1
    1. The problem statement, all variables and given/known data

    Use Euler's method with [tex]h = 1/2[/tex] to estimate [tex]y(1)[/tex] for the IVP:

    [tex]y(0)=1[/tex] [tex]y'(t)=t^2-y(t)[/tex]

    Assuming that [tex]|y(t)| \le 1[/tex] for [tex]0 \le t \le 1[/tex] determine the value of n needed to ensure that [tex]|E_n| \le 10^{-2}[/tex]

    2. Relevant equations

    [tex]|E_n| \le \frac{T}{L}(e^{L(t_n-t_0)-1})[/tex]

    3. The attempt at a solution

    The first part is easy enough:

    [tex]\Rightarrow y(1)=3/8[/tex]

    I'm having trouble with the second part. Could somebody help me out?
  2. jcsd
  3. Nov 24, 2011 #2
    Is this correct for L:


    Lipschitz with [tex]L=1[/tex]
  4. Nov 25, 2011 #3
    Please, Math Gods, I beg thee...
  5. Nov 25, 2011 #4


    User Avatar
    Science Advisor

    Yes, that's true.
  6. Nov 25, 2011 #5
    Thanks, it's T that I'm having trouble with... how would I find the upper bound for |y''(t)| ?
  7. Nov 26, 2011 #6
    Is this right?


    So, [tex]T=(1/2)*(1/2)*y''(1)=(1/4)(2(1)-1^2-3/8)=0.15625[/tex]


    [tex]E_n\le|0.15625(e-1)|\Rightarrow E_n\le 0.26848[/tex]

    Then set [tex]E_n=0.01[/tex]

    [tex]\Rightarrow 0.01 = h(0.53696)[/tex]
    [tex]\Rightarrow n ≈ 54[/tex]

    Anyone? Anyone?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook