Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative

Table 1

The numerical results of Example 8 with 𝑞=3 by formula (14) with 𝑝=3.

𝛼	ℎ	The absolute error	The convergence order
0.2	1/10	2.645451𝑒−004	—
	1/20	3.262235𝑒−005	3.0196
	1/40	4.051498𝑒−006	3.0093
	1/80	5.048441𝑒−007	3.0045
0.4	1/10	4.245164𝑒−004	—
	1/20	5.164722𝑒−005	3.0391
	1/40	6.373660𝑒−006	3.0185
	1/80	7.917542𝑒−007	3.0090
0.6	1/10	4.388473𝑒−004	—
	1/20	5.266513𝑒−005	3.0588
	1/40	6.457975𝑒−006	3.0277
	1/80	7.997522𝑒−007	3.0135
0.8	1/10	2.902946𝑒−004	—
	1/20	3.435614𝑒−005	3.0789
	1/40	4.185974𝑒−006	3.0369
	1/80	5.167862𝑒−007	3.0179