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muso07
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Homework Statement
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
Homework Equations
Adams-Moulton: [tex]x_{k+1}=x_{k}+h\Sigma ^{n}_{i=0}\beta_{i}f_{k+1-i}[/tex]
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. :)
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