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Table 3 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 × 10−4 4.513 × 10−4 9.315 × 10−6 6.678 × 10−6 2.170 × 10−10 1.007 × 10−10
0.2 1.158 × 10−3 8.536 × 10−4 4.173 × 10−5 1.352 × 10−5 4.352 × 10−10 2.568 × 10−10
0.3 3.124 × 10−3 1.421 × 10−3 6.457 × 10−5 2.098 × 10−5 6.575 × 10−10 4.123 × 10−10
0.4 5.207 × 10−3 3.521 × 10−3 7.125 × 10−5 2.983 × 10−5 8.921 × 10−10 6.348 × 10−10
0.5 7.128 × 10−3 5.326 × 10−3 8.423 × 10−5 4.130 × 10−5 1.160 × 10−9 8.457 × 10−10
0.6 3.369 × 10−2 8.459 × 10−3 9.845 × 10−5 5.725 × 10−5 1.525 × 10−9 1.253 × 10−9
0.7 5.476 × 10−2 2.823 × 10−2 1.405 × 10−4 8.054 × 10−5 2.183 × 10−9 2.159 × 10−9
0.8 6.897 × 10−2 4.106 × 10−2 2.306 × 10−4 1.157 × 10−4 3.734 × 10−9 3.458 × 10−9
0.9 9.253 × 10−2 6.456 × 10−2 5.623 × 10−4 1.701 × 10−4 7.949 × 10−9 5.442 × 10−9
1.0 2.176 × 10−1 8.036 × 10−2 7.236 × 10−4 2.560 × 10−4 1.980 × 10−8 8.864 × 10−9