Study guide: Finite difference methods for vibration problems

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Euler-Cromer is equivalent to the scheme for $u^{\prime\prime}+\omega^2u=0$

We can eliminate

$v^n$ and

$v^{n+1}$ , resulting in

$u^{n+1} = 2u^n - u^{n-1} - \Delta t^2 \omega^2u^{n}$

which is the centered finite differrence scheme for $u^{\prime\prime}+\omega^2u=0$ !