Table 8 The comparison of error norms together with the convergence rate of the present method for \(\alpha\) = 0.5, \(\sigma\) = 0.5, \(\Delta t\) = 0.00025, and \(\hat{\nu }\) = 1 at \(t\) = 1 for Example 2
From: A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation
\(M\) | Present method | Ref. [19] | Ref. [35] | Ref. [36] | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
\(\boldsymbol{L}_{2}\) | ROC | \(\boldsymbol{L}_{\infty }\) | ROC | \(\boldsymbol{L}_{2}\) | \(\boldsymbol{L}_{\infty }\) | \(\boldsymbol{L}_{2}\) | \(\boldsymbol{L}_{\infty }\) | \(\boldsymbol{L}_{2}\) | \(\boldsymbol{L}_{\infty }\) | |
10 | 4.610e−04 | – | 6.430e−04 | – | 4.353e−04 | 7.311e−04 | 1.787e−03 | 2.416e−03 | 1.4626e−05 | 1.9866e−05 |
20 | 1.141e−04 | 2.01 | 1.588e−04 | 2.02 | 1.830e−04 | 2.733e−04 | 4.403e−04 | 5.836e−04 | 1.3963e−05 | 1.9805e−05 |
40 | 2.844e−05 | 2.00 | 3.958e−05 | 2.00 | 4.198e−05 | 6.323e−05 | 9.273e−05 | 1.205e−04 | 1.3799e−05 | 1.9579e−05 |
80 | 7.099e−06 | 2.00 | 9.880e−06 | 2.00 | 1.982e−06 | 4.192e−06 | 6.221e−06 | 1.616e−05 | 1.3759e−05 | 1.9531e−05 |