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

Table 2

The numerical results of Example 7 by difference Scheme (17).

𝛼	ℎ	The absolute error	The convergence order
0.2	1/10	1.009205𝑒−006	—
	1/20	6.374128𝑒−008	3.9848
	1/40	3.988170𝑒−009	3.9984
	1/80	2.491356𝑒−010	4.007
0.4	1/10	2.982868𝑒−006	—
	1/20	1.886698𝑒−007	3.9828
	1/40	1.180691𝑒−008	3.9982
	1/80	7.375345𝑒−010	4.0008
0.6	1/10	6.568541𝑒−006	—
	1/20	4.168414𝑒−007	3.9780
	1/40	2.612079𝑒−008	3.9962
	1/80	1.632646𝑒−009	3.9999
0.8	1/10	1.281483𝑒−005	—
	1/20	8.158970𝑒−007	3.9733
	1/40	5.120258𝑒−008	3.9941
	1/80	3.202608𝑒−009	3.9989
1.2	1/10	4.091054𝑒−005	—
	1/20	2.613444𝑒−006	3.9684
	1/40	1.642689𝑒−007	3.9918
	1/80	1.028262𝑒−008	3.9978
1.4	1/10	6.933668𝑒−005	—
	1/20	4.429158𝑒−006	3.9685
	1/40	2.783972𝑒−007	3.9918
	1/80	1.742681𝑒−008	3.9978
1.6	1/10	1.145559𝑒−004	—
	1/20	7.311853𝑒−006	3.9697
	1/40	4.594486𝑒−007	3.9923
	1/80	2.875631𝑒−008	3.9980
1.8	1/10	1.850464𝑒−004	—
	1/20	1.179730𝑒−005	3.9714
	1/40	7.409938𝑒−007	3.9929
	1/80	4.637042𝑒−008	3.9982