(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the method of undetermined coefficients to derive the fourth-order Adams-Moulton formula

x_{k+1}=x_{k}+ (h/24)(9f_{k+1}+19f_{k}-5f_{k-1}+f_{k-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)=t^{2}, x(t)=t^{3}

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 f_{k}is.. Is it just the derivative of x_{k}?

edit: Nevermind, I figured it out. :)

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# Homework Help: Adams-Moulton formula

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