A Fast Compact Finite Difference Method for Fractional Cattaneo Equation Based on Caputo–Fabrizio Derivative

Table 7

Considering , the discrete error and convergence rates of u with different for Example 2.

	Order		Order		Order
0		0.0044	—	0.0044	—	0.0042	—
		2.4205e − 04	4.1841	2.3721e − 04	4.2133	2.3098e − 04	4.1845
		1.4684e − 05	4.0430	1.4390e − 05	4.0430	1.4013e − 05	4.0429
0.25		0.0027	—	0.0027	—	0.0027	—
		1.4902e − 04	4.1794	1.4894e − 04	4.1802	1.4892e − 04	4.1803
		9.0680e − 06	4.0386	9.0633e − 06	4.0386	9.0616e − 06	4.0386
0.5		0.0027	—	0.0027	—	0.0027	—
		1.4848e − 04	4.1846	1.4842e − 04	4.1852	1.4842e − 04	4.1852
		9.0323e − 06	4.0390	9.0288e − 06	4.0390	9.0286e − 06	4.0390
0.75		0.0027	—	0.0027	—	0.0027	—
		1.4902e − 04	4.1794	1.4894e − 04	4.1802	1.4892e − 04	4.1803
		9.0680e − 06	4.0386	9.0633e − 06	4.0386	9.0616e − 06	4.0386
1		0.0044	—	0.0044	—	0.0042	—
		2.4205e − 04	4.1841	2.3721e − 04	4.2133	2.3098e − 04	4.1845
		1.4684e − 05	4.0430	1.4390e − 05	4.0430	1.4013e − 05	4.0429