Table 1 Errors compared with the exact solution for Example 2
m | h (mh = 1) | \(\max |x_n -x(t_n )|\) | \(\max |y_n -y(t_n )|\) |
|---|---|---|---|
10 | 0.1 | 4.2 × 10−3 | 1.75 × 10−2 |
100 | 0.01 | 4.83 × 10−5 | 2.03 × 10−4 |
1000 | 0. 001 | 4.90 × 10−7 | 2.05 × 10−6 |
2000 | 0.0005 | 1.23 × 10−7 | 5.14 × 10−7 |
4000 | 0.00025 | 3.06 × 10−8 | 1.29 × 10−7 |
8000 | 0.000125 | 7.67 × 10−9 | 3.21 × 10−8 |
16000 | 0.0000625 | 1.92 × 10−9 | 8.04 × 10−9 |
106 | 10−6 | 9.21 × 10−12 | 3.86 × 10−11 |