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: Newtons Method - A little help

  1. Aug 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve each equation using newtons method. The problem I am working on right now is:

    [tex] x^{5}+x^{3}+x=1 [/tex]

    which is the same as:

    [tex] x^{5}+x^{3}+x-1=0 [/tex]


    2. Relevant equations

    [tex] x_{2} = x_{1}-\frac {f(x)}{f'(x)} [/tex]

    with x1 being the first guess to what an f(x)=0 would be.

    3. The attempt at a solution

    So I put the equation into my calculator to graph it and It is very clear from the graph that f(x)=0 on the x>0 side so I choose x1=1 and continue like so:

    [tex] x_{2} = 1 - \frac {f(x)}{f'(x)} = 1- \frac {2}{9} = \frac {7}{9} [/tex]

    and after 5 iterations I get:

    [tex] x_{5} = .6368843716 [/tex]

    which looks right to me but when I check the answer in the back of the book it says that it should be -.63688, so just the opposite of what I got. The graph of the equation clearly shows that f(x)=0 on x>0 so did I do something wrong or does the book have another typo?

    thanks
     
  2. jcsd
  3. Aug 2, 2010 #2

    Char. Limit

    User Avatar
    Gold Member

    Another typo.
     
  4. Aug 3, 2010 #3

    hunt_mat

    User Avatar
    Homework Helper

    I've just spent the last 5 months play with Newton's method... The general method is
    [tex]
    x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}
    [/tex]
    Where in your case:
    [tex]
    f(x)=x^{5}+x^{3}+x-1
    [/tex]
    The derivative of this is:
    [tex]
    f'(x)=5x^{4}+3x^{2}+1
    [/tex]
    And in your case Newton's method is
    [tex]
    x_{n+1}=x_{n}-\frac{x_{n}^{5}+x_{n}^{3}+x_{n}-1}{5x_{n}^{4}+3x_{n}^{2}+1}
    [/tex]
    So all you have to do is plug numbers in. Newtons method converges very quickly in my experience, 2 or 3 iterations will usually do the trick.
     
  5. Aug 3, 2010 #4

    hunt_mat

    User Avatar
    Homework Helper

    As a check, plug your solution back into the equation and check.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook