Theory and Modern Applications
Table 5 Absolute and relative errors of Example 5.3 at \(\alpha =1\)
t | Exact solution | RK solution | Absolute error | Relative error |
|---|---|---|---|---|
0.0 | 1.0 | 1.0 | 0.0 | 0.0 |
0.1 | 0.904837 | 0.904877 | 3.95866 × 10−5 | 4.37499 × 10−5 |
0.2 | 0.818731 | 0.818818 | 8.72577 × 10−5 | 1.06577 × 10−4 |
0.3 | 0.740818 | 0.740951 | 1.32383 × 10−4 | 1.78698 × 10−4 |
0.4 | 0.670320 | 0.670493 | 1.73199 × 10−4 | 2.58382 × 10−4 |
0.5 | 0.606531 | 0.606738 | 2.07475 × 10−4 | 3.42069 × 10−4 |
0.6 | 0.548812 | 0.549045 | 2.33234 × 10−4 | 4.24980 × 10−4 |
0.7 | 0.496585 | 0.496835 | 2.49262 × 10−4 | 5.01953 × 10−4 |
0.8 | 0.449329 | 0.449584 | 2.55378 × 10−4 | 5.68354 × 10−4 |
0.9 | 0.406570 | 0.406822 | 2.52431 × 10−4 | 6.20880 × 10−4 |
1.0 | 0.367879 | 0.368122 | 2.42089 × 10−4 | 6.58065 × 10−4 |