From: Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations
x | PQSM (k = 0.002) | QBSGM [4] (k = 0.00025) | Exact | ||||
---|---|---|---|---|---|---|---|
n = 20 | n = 40 | n = 80 | n = 20 | n = 40 | n = 80 | ||
0.1 | 1.105145 | 1.105166 | 1.105171 | 1.105287 | 1.105216 | 1.105197 | 1.105170918 |
0.2 | 1.221357 | 1.221394 | 1.221403 | 1.221644 | 1.221493 | 1.221455 | 1.221402758 |
0.3 | 1.349794 | 1.349846 | 1.349860 | 1.350217 | 1.349992 | 1.349935 | 1.349858808 |
0.4 | 1.491745 | 1.491809 | 1.491825 | 1.492287 | 1.491996 | 1.491922 | 1.491824698 |
0.5 | 1.648629 | 1.648703 | 1.648722 | 1.649270 | 1.648922 | 1.648838 | 1.648721271 |
0.6 | 1.822021 | 1.822099 | 1.822119 | 1.822727 | 1.822342 | 1.822247 | 1.822118800 |
0.7 | 2.013657 | 2.013733 | 2.013753 | 2.014378 | 2.013979 | 2.013882 | 2.013752707 |
0.8 | 2.225462 | 2.225523 | 2.225541 | 2.226118 | 2.225747 | 2.225661 | 2.225540928 |
0.9 | 2.459564 | 2.459593 | 2.459603 | 2.460020 | 2.459745 | 2.459680 | 2.459603111 |
\({L}_{{2}}\) | 3.11 × 10−4 | 9.06 × 10−5 | 3.90 × 10−6 | 8.48 × 10−4 | 1.62 × 10−4 | 9.26 × 10−5 | |
\({L}_{{\infty}} \) | 9.83 × 10−5 | 2.04 × 10−5 | 7.16 × 10−7 | 6.25 × 10−4 | 2.27 × 10−4 | 1.33 × 10−4 |