md2011-03-note_Part_6

md2011-03-note_Part_6 - Hence in essence the algorithm...

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I Hence, in essence, the algorithm works as { r ( t ) , a ( t ) , r ( t - Δ t ) } { r ( t + Δ t ) , a ( t + Δ t ) } . I The missing velocities can be calculated as: v ( t ) = r ( t + Δ t ) - r ( t - Δ t ) 2 Δ t . I The error made per iteration is O ( Δ t 4 ) – for the velocities O ( Δ t 2 ) . Notes

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I Memory requirement is O ( 9 N ) (quite compact). I Verlet algorithm conserves energy, but has some numerical problems (mainly due to adding a small number O ( Δ t 2 ) to much larger values in eq. 13). I Also the linear momentum is conserved because of the conservative forces ( a ( t ) is always directly calculated from the forces). I Because of the symmetric usage of r ( t + Δ t ) and r ( t - Δ t ) the algorithm is time reversible. I However, the velocity handling is awkward ( r ( t + Δ t ) is needed for v ( t ) ). Notes
L±²³-F´µ¶ V±´·±¸ I This algorithm was invented in order to tackle some of the problems of the standard Verlet. I

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md2011-03-note_Part_6 - Hence in essence the algorithm...

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