Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives

Table 1

The numerical results of Example 6 by difference Scheme (7).

𝛼	ℎ	The absolute error	The convergence order
0.2	1/10	1.507793𝑒−006	—
	1/20	9.410104𝑒−008	4.0021
	1/40	5.876619𝑒−009	4.0012
	1/80	3.671357𝑒−010	4.0006
0.4	1/10	2.250905𝑒−006	—
	1/20	1.402929𝑒−007	4.0040
	1/40	8.755965𝑒−009	4.0020
	1/80	5.468621𝑒−010	4.0010
0.6	1/10	2.154827𝑒−006	—
	1/20	1.342424𝑒−007	4.0047
	1/40	8.377252𝑒−009	4.0022
	1/80	5.231917𝑒−010	4.0011
0.8	1/10	1.313317𝑒−006	—
	1/20	8.185957𝑒−008	4.0039
	1/40	5.110355𝑒−009	4.0017
	1/80	3.192508𝑒−010	4.0007
1.2	1/10	1.371602𝑒−006	—
	1/20	8.576212𝑒−008	3.9994
	1/40	5.363498𝑒−009	3.9991
	1/80	3.354046𝑒−010	3.9992
1.4	1/10	2.337915𝑒−006	—
	1/20	1.464272𝑒−007	3.9970
	1/40	9.165078𝑒−009	3.9979
	1/80	5.734311𝑒−010	3.9985
1.6	1/10	2.507873𝑒−006	—
	1/20	1.572017𝑒−007	3.9958
	1/40	9.842569𝑒−009	3.9974
	1/80	6.154188𝑒−010	3.9994
1.8	1/10	1.690729𝑒−006	—
	1/20	1.059074𝑒−007	3.9968
	1/40	6.627397𝑒−009	3.9982
	1/80	4.135963𝑒−010	4.0021