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Table 3 Numerical results of FRPS method of Example 4.2

From: Construction of fractional power series solutions to fractional stiff system using residual functions algorithm

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