Table 11 The comparison of present, existing, and exact solutions with \(\sigma\) = 0.5, \(\alpha\) = 0.5, \(\Delta t\) = 0.00025, and \(\hat{\nu }\) = 1 for Example 3
From: A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation
x | Present M = 40 | QBSG [19] M = 40 | Present M = 80 | QBSG [19] M = 80 | Exact |
|---|---|---|---|---|---|
0.0 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
0.1 | 0.587374 | 0.585106 | 0.587682 | 0.587257 | 0.587785 |
0.2 | 0.950372 | 0.947079 | 0.950885 | 0.950262 | 0.951057 |
0.3 | 0.950349 | 0.947320 | 0.950879 | 0.950310 | 0.951057 |
0.4 | 0.587336 | 0.585586 | 0.587673 | 0.587348 | 0.587785 |
0.5 | 0.000000 | 0.000001 | 0.000000 | 0.000000 | 0.000000 |
0.6 | − 0.587336 | − 0.585584 | − 0.587673 | − 0.587346 | − 0.587785 |
0.7 | − 0.950349 | − 0.947318 | − 0.950879 | − 0.950310 | − 0.951057 |
0.8 | − 0.950372 | − 0.947078 | − 0.950885 | − 0.950260 | − 0.951057 |
0.9 | − 0.587374 | − 0.585106 | − 0. 0.587682 | − 0.587257 | − 0.587785 |
1.0 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
\(L_{2}\) | 5.176643e−04 | 2.899412e−03 | 1.293988e−04 | 5.77143e−04 | |
\(L_{\infty }\) | 7.313814e−04 | 4.063808e−03 | 1.830408e−04 | 8.13220e−04 |