# 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