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

Table 6

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

	Order		Order		Order
1		7.3224e − 05	—	5.5643e − 05	—	3.8478e − 05	—
		4.5707e-06	4.0018	3.4695e − 06	4.0034	2.3900e − 06	4.0090
		2.8558e − 07	4.0004	2.1671e − 07	4.0009	1.4913e − 07	4.0024
		1.7847e − 08	4.0001	1.3543e − 08	4.0001	9.3169e − 09	4.0006
0.1		0.0012	—	0.0012	—	0.0012	—
		7.0462e − 05	4.0900	6.9731e − 05	4.1051	6.9007e − 05	4.1201
		4.3571e − 06	4.0154	4.3110e − 06	4.0157	4.2650e − 06	4.0161
		2.7160e − 07	4.0038	2.6871e − 07	4.0039	2.6583e − 07	4.0040
0.01		0.0090	—	0.0090	—	0.0090	—
		4.9257e − 04	4.1915	4.9235e − 04	4.1922	4.9232e − 04	4.1923
		2.9868e − 05	4.0437	2.9855e − 05	4.0436	2.9854e − 05	4.0436
		1.8531e − 06	4.0106	1.8523e − 06	4.0106	1.8522e − 06	4.0106