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Leapfrog, Cont'd
Complication: need to "jumpstart" and "resync"...
- vi+1/2 = vi + ½ t f(xi) [opening "kick": Euler]
- xi+1 = xi + vi+1/2 t ["drift"]
- vi+1 = vi+1/2 + ½ t f(xi+1) [closing "kick": resync]
- Note vi+3/2 = vi+1 + ½ t f(xi+1) = vi+1/2 + t f(xi+1).
Also have "drift-kick-drift" (DKD) scheme.
Like midpoint method, Leapfrog is second order.
So why is Leapfrog so great?...
Notes: