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Adams-Moulton formula

  1. May 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Use the method of undetermined coefficients to derive the fourth-order Adams-Moulton formula
    xk+1=xk+ (h/24)(9fk+1+19fk-5fk-1+fk-2

    2. Relevant equations
    Adams-Moulton: [tex]x_{k+1}=x_{k}+h\Sigma ^{n}_{i=0}\beta_{i}f_{k+1-i}[/tex]

    3. The attempt at a solution
    It has to be exact for x(t)=1, x(t)=t, x(t)=t2, x(t)=t3

    So I have to solve for the coefficients of [tex]x_{k+1}=x_{k}+h(\beta_{0}f_{k+1} + \beta_{1}f_{k} + \beta_{2}f_{k-1} + \beta_{3}f_{k-2})[/tex]

    I know I need to set up a system of equations, but I'm confused as to what fk is.. Is it just the derivative of xk?

    edit: Nevermind, I figured it out. :)
    Last edited: May 30, 2010
  2. jcsd
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