S0

Numerical

algorithm

n = 200

Numerical

algorithm

n = 1000

Monte Carlo

simulation

Times = 106

Milev’s Num.

algorithm

n = 1000

Milev’s M.C.

simulation

times = 107

95

0.018879

(6.359e−4)

0.019397

(1.178e−4)

-

0.019528

-

95.0001

0.018879

(6.359e−4)

0.019397

(1.178e−4)

0.018508

(0.00033)

0.019528

0.019515

(0.00021)

100

0.041751

(1.182e−3)

0.042716

(2.184e−4)

0.043521

(0.00051)

0.042957

0.042736

(0.00031)

109.9999

0.018067

(6.086e−4)

0.018563

(1.128e−4)

0.018853

(0.00033)

0.018688

0.018676

(0.00019)

110

0.018067

(6.086e−4)

0.018563

(1.128e−4)

-

0.018688

-

CPU

87 ms

407 ms

1643 s

9 s

hundred sec.