0.00 0.02 0.04 0.06 0.08 0.10Time

-2.0

-1.5

-1.0

-0.5

0.0Na

tura

l Log

of T

otal

Kin

etic

Ener

gy (E

/E0)

Analyticaldt=0.0025dt=0.00125dt=0.000625

10-4 10-3 10-2

Time Step Size

10-6

10-5

10-4

10-3

Erro

r

0.0 20.0 40.0 60.0 80.0 100.0Time

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

Natu

ral L

og o

f Ene

rgy

Ratio

10th OrderLinear Theory8th Order14th Order