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Table 4 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 5.425 × 10−1 4.215 × 10−1 9.914 × 10−2 9.807 × 10−2 9.74098 × 10−2 6.206 × 10−2
0.2 6.456 × 10−1 5.452 × 10−1 2.243 × 10−1 1.968 × 10−1 1.95502 × 10−1 8.245 × 10−2
0.3 8.425 × 10−1 6.152 × 10−1 3.654 × 10−1 2.980 × 10−1 2.96196 × 10−1 1.312 × 10−1
0.4 8.896 × 10−1 7.431 × 10−1 5.756 × 10−1 4.049 × 10−1 4.02421 × 10−1 2.318 × 10−1
0.5 9.476 × 10−1 8.189 × 10−1 7.265 × 10−1 5.219 × 10−1 5.18782 × 10−1 3.436 × 10−1
0.6 3.523 × 10−0 1.078 × 10−0 8.438 × 10−1 6.558 × 10−1 6.51931 × 10−1 4.540 × 10−1
0.7 4.247 × 10−0 3.368 × 10−0 9.457 × 10−1 8.164 × 10−1 8.11499 × 10−1 7.243 × 10−1
0.8 6.235 × 10−0 4.236 × 10−0 1.214 × 10−0 1.017 × 10−0 1.01174 × 10−0 9.345 × 10−1
0.9 7.369 × 10−0 5.348 × 10−0 2.125 × 10−0 1.282 × 10−0 1.27442 × 10−0 1.895 × 10−0
1.0 8.563 × 10−0 6.831 × 10−0 4.425 × 10−0 1.644 × 10−0 1.63398 × 10−0 2.213 × 10−0