Theory and Modern Applications
Table 3 Numerical results of FRPS method of Example 4.2
t | Exact u(t) | Approximation u(t) | Absolute Error | Relative Error |
|---|---|---|---|---|
0. | 1. | 1. | 0. | 0. |
0.2 | 0.6703200460356 | 0.67032004603564 | 0. | 0. |
0.4 | 0.4493289641172 | 0.44932896411722 | 5.5511151231 × 10−17 | 1.2354233905 × 10−16 |
0.6 | 0.301194211912 | 0.30119421191220 | 0. | 0. |
0.8 | 0.2018965179947 | 0.201896517994656 | 5.5511151231 × 10−16 | 2.7494853196 × 10−15 |
1.0 | 0.1353352832366 | 0.135335283236650 | 3.7581049384 × 10−14 | 2.7768848215 × 10−13 |
1.2 | 0.0907179532894 | 0.090717953291115 | 1.7021939414 × 10−12 | 1.8763584050 × 10−11 |
1.4 | 0.0608100626252 | 0.060810062667847 | 4.2628810204 × 10−11 | 7.0101572608 × 10−10 |
1.6 | 0.0407622039784 | 0.040762204671022 | 6.9265617547 × 10−10 | 1.6992608541 × 10−8 |
1.8 | 0.0273237224473 | 0.027323730534706 | 8.0874130483 × 10−9 | 2.9598503878 × 10−7 |
2. | 0.0183156388887 | 0.018315711651223 | 7.27624886870 × 10−8 | 3.9726972741 × 10−6 |
t | Exact v(t) | Approximation v(t) | Absolute Error | Relative Error |
|---|---|---|---|---|
0. | 1. | 1. | 0. | 0. |
0.2 | 0.8187307531 | 0.8187307530780 | 0. | 0. |
0.4 | 0.6703200460 | 0.6703200460356 | 0. | 0. |
0.6 | 0.5488116361 | 0.5488116360940 | 0. | 0. |
0.8 | 0.4493289641 | 0.4493289641172 | 5.55111512313 × 10−17 | 1.23542339053 × 10−16 |
1.0 | 0.3678794412 | 0.3678794411714 | 5.55111512313 × 10−17 | 1.50894953669 × 10−16 |
1.2 | 0.301194212 | 0.3011942119122 | 0. | 0. |
1.4 | 0.2465969639 | 0.2465969639416 | 1.38777878078 × 10−16 | 5.627720465813 × 10−16 |
1.6 | 0.2018965180 | 0.2018965179947 | 5.551115123126 × 10−16 | 2.74948531964 × 10−15 |
1.8 | 0.1652988882 | 0.1652988882216 | 4.21884749358 × 10−15 | 2.55225400423 × 10−14 |
2. | 0.1353352832 | 0.1353352832367 | 3.75810493836 × 10−14 | 2.77688482152 × 10−13 |