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Table 2 Absolute error of variance 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 1.425 × 10−3 7.356 × 10−4 3.914 × 10−5 1.149 × 10−5 7.045 × 10−6 3.206 × 10−6
0.2 3.356 × 10−3 1.108 × 10−3 7.243 × 10−5 4.312 × 10−5 1.467 × 10−5 6.542 × 10−6
0.3 8.147 × 10−3 2.006 × 10−3 9.568 × 10−5 6.452 × 10−5 2.354 × 10−5 8.312 × 10−6
0.4 2.267 × 10−2 3.876 × 10−3 9.809 × 10−5 7.765 × 10−5 3.456 × 10−5 1.318 × 10−5
0.5 4.476 × 10−2 6.189 × 10−3 5.539 × 10−5 8.826 × 10−5 4.901 × 10−5 2.894 × 10−5
0.6 6.523 × 10−2 1.078 × 10−2 8.438 × 10−5 9.105 × 10−5 6.886 × 10−5 4.364 × 10−5
0.7 8.045 × 10−2 4.368 × 10−2 4.308 × 10−4 1.432 × 10−4 9.724 × 10−5 6.157 × 10−5
0.8 1.158 × 10−1 6.456 × 10−2 1.214 × 10−3 2.565 × 10−4 1.393 × 10−4 8.364 × 10−5
0.9 3.369 × 10−1 8.564 × 10−2 2.927 × 10−3 8.253 × 10−4 2.038 × 10−4 1.421 × 10−4
1.0 4.158 × 10−1 1.831 × 10−1 6.624 × 10−3 2.567 × 10−3 3.059 × 10−4 1.897 × 10−4