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Theory and Modern Applications

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