Theory and Modern Applications
Table 3 Comparison results of the Riccati equation in problem 2 for
From: Fractional-order Riccati differential equation: Analytical approximation and numerical results
t | LAPM α = 1 | Exact solution | Absolute error |
|---|---|---|---|
y(t) | y(t) | ||
1.0 | 0.7615941560 | 0.7615941560 | 0.01235728510 × 10−13 |
2.0 | 0.9640275801 | 0.9640275801 | 0.00524212251 × 10−12 |
3.0 | 0.9950547537 | 0.9950547537 | 0.00816114713 × 10−12 |
4.0 | 0.9993292997 | 0.9993292997 | 1.15746178216 × 10−12 |
5.0 | 0.9999092043 | 0.9999092043 | 6.17826138530 × 10−11 |
6.0 | 0.9999877117 | 0.9999877117 | 4.55279023510 × 10−11 |
7.0 | 0.9999983377 | 0.9999983369 | 7.57246128510 × 10−10 |
8.0 | 0.9999997813 | 0.9999997749 | 6.33977368904 × 10−9 |
9.0 | 1.0000000063 | 0.9999999695 | 3.67962922016 × 10−8 |
10.0 | 1.0000001574 | 0.9999999958 | 1.61485463823 × 10−7 |
15.0 | 1.000000000 | 1.0000000000 | 0.00002076502676 |
20.0 | 1.0000000000 | 1.0000000000 | 0.00030117782151 |
25.0 | 1.0000000000 | 1.0000000000 | 0.00161702848408 |
30.0 | 1.0000000000 | 1.0000000000 | 0.00510751644687 |