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Table 1 Absolute error of the expectation of \(\pmb{X(t)}\) with the Euler, RK2, and RK4 methods and \(\pmb{h=\frac{1}{20}}\) , \(\pmb{h=\frac{1}{50}}\)

From: Mean square numerical solution of stochastic differential equations by fourth order Runge-Kutta method and its application in the electric circuits with noise

t Euler RK2 RK4
\(\boldsymbol {h=\frac{1}{20}}\) \(\boldsymbol {h=\frac{1}{50}}\) \(\boldsymbol {h=\frac{1}{20}}\) \(\boldsymbol {h=\frac{1}{50}}\) \(\boldsymbol {h=\frac{1}{20}}\) \(\boldsymbol {h=\frac{1}{50}}\)
0.1 7.548 × 10−3 4.463 × 10−3 5.315 × 10−5 2.421 × 10−5 1.253 × 10−8 1.007 × 10−8
0.2 9.157 × 10−3 6.128 × 10−3 1.173 × 10−4 6.548 × 10−5 2.427 × 10−8 1.568 × 10−8
0.3 1.253 × 10−2 8.421 × 10−3 2.074 × 10−4 1.104 × 10−4 3.523 × 10−8 2.123 × 10−8
0.4 2.107 × 10−2 1.058 × 10−2 3.433 × 10−4 2.352 × 10−4 4.602 × 10−8 3.312 × 10−8
0.5 3.257 × 10−2 2.108 × 10−2 5.541 × 10−4 3.425 × 10−4 5.928 × 10−8 4.986 × 10−8
0.6 4.369 × 10−2 3.249 × 10−2 8.845 × 10−4 5.124 × 10−4 8.100 × 10−8 6.253 × 10−8
0.7 5.578 × 10−2 4.823 × 10−2 1.405 × 10−3 7.461 × 10−4 1.241 × 10−7 8.159 × 10−8
0.8 8.457 × 10−2 6.467 × 10−2 2.229 × 10−3 1.253 × 10−3 2.180 × 10−7 1.109 × 10−7
0.9 1.253 × 10−1 8.812 × 10−2 3.539 × 10−3 1.895 × 10−3 4.209 × 10−7 2.542 × 10−7
1.0 2.346 × 10−1 1.439 × 10−1 5.637 × 10−3 2.764 × 10−3 8.506 × 10−7 4.864 × 10−7