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Table 3 Processing times of System 4

From: A higher-order numerical framework for stochastic simulation of chemical reaction systems

   

τ

  
 

0.005

0.010

0.020

0.040

0.08

ETL

191 (16.7)

82.3 (34.5)

46 (76.1)

32.6 (188.5)

19.7 (630.1)

xETL

-

293 (1.1)

123 (7.2)

66.4 (36.3)

35.1 (253.1)

xxETL

-

-

279 (0.93)

152 (2.5)

80.1 (36.0)

MPTL

165 (1.3)

84 (3.6)

44.9 (15.0)

24.1 (65.5)

12.3 (257.1)

xMPTL

-

244 (1.0)

129 (7.7)

69.1 (35.5)

36.3 (126.2)

xxMPTL

-

-

(-MC) 289 (1.2)

(-MC) 153 (1.5)

81.3 (5.3)

TTTL

277 (1.2)

155 (3.5)

82.4 (13.5)

44.6 (58.1)

23.3 (90.0)

xTTTL

-

(-MC) 430 (0.41)

(-MC) 239 (0.15)

128 (1.4)

68 (107.5)

xxTTTL

-

-

(-MC) 515 (0.45)

(-MC) 283 (0.37)

(-MC) 151 (16.9)

  1. Processing times (in thousands of seconds) of 107 simulations of System 4 using Euler τ-leap, midpoint τ-leap and ??-trapezoidal τ-leap methods and their extrapolated and double-extrapolated versions. Absolute errors in the mean of X1from the SSA values are included in brackets. Running 107 simulations of an SSA using the Direct Method would take approximately 1.47 × 107 seconds. Entries marked (-MC) are thought to be below the Monte Carlo error level; bold entries are faster than the un/single-extrapolated versions with similar error level (i.e. compare with one row above).