A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation

Beni-Suef University Journal of Basic and Applied Sciences

Table 12 The comparison of present, existing, and exact solutions with \(\sigma\) = 0.5, \(\alpha\) = 0.5, \(M\) = 120, and \(\hat{\nu }\) = 1 at \(t\) = 1 for Example 3

	Present	QBSG [19]	Present	QBSG [19]	Present	QBSG [19]	Present	QBSG [19]	Exact
\(\boldsymbol{x}\)	\(\boldsymbol{\Delta t}\) = 0.0025		\(\boldsymbol{\Delta t}\) = 0.002		\(\boldsymbol{\Delta t}\) = 0.001		\(\boldsymbol{\Delta t}\) = 0.0005
0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
0.1	0.587705	0.588970	0.587708	0.588675	0.587719	0.588083	0.587729	0.587788	0.587785
0.2	0.950923	0.952952	0.950927	0.952484	0.950945	0.951545	0.950963	0.951076	0.951057
0.3	0.950916	0.952914	0.950922	0.952458	0.950940	0.951544	0.950959	0.951086	0.951057
0.4	0.587695	0.588914	0.587698	0.588635	0.587711	0.588087	0.587723	0.587810	0.587785
0.5	0.000000	0.000005	0.000000	0.000005	0.000000	0.000005	0.000000	0.000004	0.000000
0.6	− 0.587695	− 0.588905	− 0.587698	− 0.588630	− 0.587711	− 0.588077	− 0.587723	− 0.587801	− 0.587785
0.7	− 0.950916	− 0.952912	− 0.950922	− 0.952456	− 0.950940	− 0.951540	− 0.950959	− 0.951084	− 0.951057
0.8	− 0.950923	− 0.952949	− 0.950927	− 0.952479	− 0.950945	− 0.951540	− 0.950963	− 0.951070	− 0.951057
0.9	− 0.587705	− 0.588968	− 0.587708	− 0.588672	− 0.587719	− 0.588080	− 0.587729	− 0.587784	− 0.587785
1.0	0.000000	0.000000	− 0.587708	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
\(L_{2}\)	1.0200e−04	1.39237e−03	9.7988e−05	1.04859e−03	8.4639e−05	3.5948e−04	7.0823e−05	1.7823e−05
\(L_{\infty }\)	1.4438e−04	1.97435e−03	1.3870e−04	1.48780e−03	1.1979e−04	5.1210e−04	1.0022e−04	3.2161e−05