A High-Accuracy MOC/FD Method for Solving Fractional Advection-Diffusion Equations

Table 1

The errors and ratios in space calculated by CFDM (12) with 𝑑=0.1 and Δ𝑡=1/400 at time 𝑡=1.5, for two different fractional orders 𝛼=1.9 and 1.6, respectively.

	Δ𝑥	‖𝐸‖∞-CFDM	Ratio	‖𝐸‖2-CFDM	Ratio
𝛼=1.9	1/25	8.9731𝐸−2	—	7.4998𝐸−2	—
	1/30	7.5702𝐸−2	0.9325	6.2978𝐸−2	0.9581
	1/35	6.5100𝐸−2	0.9788	5.3975𝐸−2	1.0001
	1/40	5.6805𝐸−2	1.0207	4.6976𝐸−2	1.0401
	1/45	5.0149𝐸−2	1.0581	4.1379𝐸−2	1.0771
𝛼=1.6	1/60	1.0621𝐸−1	—	7.1299𝐸−2	—
	1/65	9.7561𝐸−2	1.0612	6.5310𝐸−2	1.0961
	1/70	8.9922𝐸−2	1.1002	6.0045𝐸−2	1.1342
	1/75	8.3116𝐸−2	1.1408	5.5381𝐸−2	1.1720
	1/80	7.7015𝐸−2	1.1813	5.1218𝐸−2	1.2108