Table 3 The \(L_{2}\) and \(L_{\infty }\) errors with \(\alpha\) = 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
\(M\) | \(L_{2}\) | \(L_{\infty }L_{\infty }\) | ||||||
|---|---|---|---|---|---|---|---|---|
Present | QBSG method [19] | Present | QBSG method [19] | |||||
\({\boldsymbol{\sigma}}\) = 0.1 | \({\boldsymbol{\sigma}}\) = 0.5 | \({\boldsymbol{\sigma}}\) = 0.9 | \({\boldsymbol{\sigma}}\) = 0.1 | \({\boldsymbol{\sigma}}\) = 0.5 | \({\boldsymbol{\sigma}}\) = 0.9 | |||
10 | 2.59e−04 | 6.34e−05 | 5.23e−06 | 1.6329e−03 | 3.42e−04 | 8.37e−05 | 6.90e−06 | 2.2967e−03 |
20 | 6.47e−05 | 1.59e−05 | 1.25e−06 | 4.4772e−04 | 8.59e−05 | 2.11e−05 | 1.66e−06 | 6.2502e−04 |
40 | 1.62e−05 | 4.00e−06 | 2.78e−07 | 1.6183e−04 | 2.15e−05 | 5.32e−06 | 3.67e−07 | 2.2735e−04 |
80 | 4.08e−06 | 1.03e−06 | 3.65e−08 | 1.1255e−05 | 5.42e−06 | 1.37e−06 | 4.72e−08 | 1.3312e−04 |