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Euler-Cromer is equivalent to the scheme for u^{\prime\prime}+\omega^2u=0
- Forward Euler and Backward Euler have error \Oof{\Delta t}
- What about the overall scheme? Expect \Oof{\Delta t} ...
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 !
