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!

Numerical Recipes Eq. 9.4.6!

  1. Sep 22, 2010 #1
    1. The problem statement, all variables and given/known data

    I want to derive equation Eq. 9.4.6 in Numerical Recipes from the expressions given, as stated in the book!
    The equation represents the next (i+1 th) deviation [tex]\epsilon[/tex] from the true root.
    Eq. 9.4.6:

    [tex]
    \epsilon_{i+1} = -\epsilon_i^2 \frac{f''(x)}{2f'(x)}
    [/tex]

    2. Relevant equations

    Eq. 9.4.5:

    [tex]
    \epsilon_{i+1} = \epsilon_i + \frac{f(x_i)}{f'(x_i)}
    [/tex]

    [tex]\epsilon_i[/tex] represents deviation from true root.


    General Taylor expansion:

    Eq. 9.4.3:
    [tex]
    f(x+\epsilon) = f(x) + \epsilon f'(x) + ...
    [/tex]

    [tex]
    f'(x+\epsilon) = f'(x) + \epsilon f''(x) + ...
    [/tex]



    3. The attempt at a solution

    [tex]
    \epsilon_{i+1} = \epsilon_i^2 \frac{f''(x)}{f'(x) + \epsilon_i f''(x)}
    [/tex]

    but this is not equation 9.4.6! Please help!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted
Similar Discussions: Numerical Recipes Eq. 9.4.6!
  1. Thevenin's Eq. Circuit (Replies: 9)

  2. Numeric Integration (Replies: 0)

  3. Write Differential Eq ? (Replies: 12)

Loading...