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Homework Help: Newton method

  1. Nov 7, 2009 #1
    1. The problem statement, all variables and given/known data

    If I have a non linear integral equation of the form:


    and i want to find a way to solve this numerically using the newton method

    2. Relevant equations

    3. The attempt at a solution

    after discretizing, and using the quadrature rule, i have:

    [tex]y(s_i)+\sum^i_{j=0}{w_j K(x_i,s_j,y(s_j)}ds=f(x_i)[/tex]

    but i am struggling on knowing what the weights wj should be using the newton procedure.

    Thank you in advance.
  2. jcsd
  3. Nov 8, 2009 #2
    sorry, it should be
    [tex]y_i+\sum^i_{j=0}{w_j K(x_i,x_j,y_j)}=f(x_i)[/tex]
    where y_i means y(x_i)
    I can use the trapezoidal scheme and then i have:

    but how can this be solved when i need to know y_i to get y_i since y_i is in the last term of the right hand side?
    since i cant make y_i as the subject.
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