Table 4 The numerical solutions with \(\sigma\) = 0.5, \(\alpha\) = 0.5, \(M\) = 80, 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 | QBSG method [19] | Present method | QBSG method [19] | Present method | QBSG method [19] | Present method | QBSG method [19] |
|---|---|---|---|---|---|---|---|---|
\({\boldsymbol{\Delta}} t =\) 0.002 | \({\boldsymbol{\Delta}} t =\) 0.001 | \({\boldsymbol{\Delta}} t =\) 0.0005 | \({\boldsymbol{\Delta}} t =\) 0.00025 | |||||
0.0 | 1.000 | 1.000000 | 1.0000 | 1.000000 | 1.0000 | 1.000000 | 1.0000 | 1.000000 |
0.1 | 1.1052 | 1.105356 | 1.1052 | 1.105287 | 1.1052 | 1.105216 | 1.1052 | 1.105197 |
0.2 | 1.2214 | 1.221768 | 1.2214 | 1.221644 | 1.2214 | 1.221493 | 1.2214 | 1.221455 |
0.3 | 1.3499 | 1.350395 | 1.3499 | 1.350217 | 1.3499 | 1.349992 | 1.3499 | 1.349935 |
0.4 | 1.4918 | 1.492516 | 1.4918 | 1.492287 | 1.4918 | 1.491996 | 1.4918 | 1.491922 |
0.5 | 1.6487 | 1.649543 | 1.6487 | 1.649270 | 1.6487 | 1.648922 | 1.6487 | 1.648838 |
0.6 | 1.8221 | 1.823031 | 1.8221 | 1.822727 | 1.8221 | 1.822342 | 1.8221 | 1.822247 |
0.7 | 2.0138 | 2.014687 | 2.0138 | 2.014378 | 2.0138 | 2.013979 | 2.0138 | 2.013882 |
0.8 | 2.2255 | 2.226387 | 2.2255 | 2.226118 | 2.2255 | 2.225747 | 2.2255 | 2.225661 |
0.9 | 2.4596 | 2.460180 | 2.4596 | 2.460020 | 2.4596 | 2.459745 | 2.4596 | 2.459680 |
1.0 | 2.7183 | 2.718282 | 2.7183 | 2.718282 | 2.7183 | 2.718282 | 2.7183 | 2.718282 |