Table 2 The comparison of present and existing numerical solutions with exact solutions for \(\alpha\) = 0.5, \(\sigma\) = 0.5, \(\Delta t\) = 0.00025, and \(\hat{\nu }\) = 1 at \(t\) = 1
From: A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation
\(x\) | Present method M = 10 | QBSG method [19] M = 10 | Present method M = 20 | QBSG method [19] M = 20 | Present method M = 40 | QBSG method [19] M = 40 | Present method M = 80 | QBSG method [19] M = 80 | Exact |
|---|---|---|---|---|---|---|---|---|---|
0.0 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
0.1 | 1.105304 | 1.105440 | 1.105204 | 1.105287 | 1.105179 | 1.105216 | 1.105173 | 1.105197 | 1.105171 |
0.2 | 1.221651 | 1.222203 | 1.221465 | 1.221644 | 1.221418 | 1.221493 | 1.221407 | 1.221455 | 1.221403 |
0.3 | 1.350204 | 1.351078 | 1.349946 | 1.350217 | 1.349880 | 1.349992 | 1.349864 | 1.349935 | 1.349859 |
0.4 | 1.492247 | 1.493437 | 1.491908 | 1.492287 | 1.491851 | 1.491996 | 1.491831 | 1.491922 | 1.491825 |
0.5 | 1.649197 | 1.650663 | 1.648841 | 1.649270 | 1.648751 | 1.648922 | 1.648729 | 1.648838 | 1.648721 |
0.6 | 1.822618 | 1.824294 | 1.822244 | 1.822727 | 1.822150 | 1.822342 | 1.822127 | 1.822247 | 1.822119 |
0.7 | 2.014238 | 2.016049 | 2.013874 | 2.014378 | 2.013783 | 2.013979 | 2.013760 | 2.013882 | 2.013753 |
0.8 | 2.225958 | 2.227650 | 2.225645 | 2.226118 | 2.225567 | 2.225747 | 2.225547 | 2.225661 | 2.225541 |
0.9 | 2.459872 | 2.461512 | 2.459670 | 2.460020 | 2.459620 | 2.459745 | 2.459607 | 2.459680 | 2.459603 |
1.0 | 2.718282 | 2.718282 | 2.718282 | 2.718282 | 2.718282 | 2.718282 | 2.718282 | 2.718282 | 2.718282 |