A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

Table 1

Maximum absolute error, with various choices of 𝑁, for Example 4 in which 𝑥∈[0,10].

𝑁	𝛼	𝛽	𝜈	MGLT(G)	MGLT(GR)	𝜈	MGLT(G)	MGLT(GR)	𝜈	MGLT(G)	MGLT(GR)
10	0	2	0.1	1.32⋅10^−2	2.24⋅10^−2	0.5	8.48⋅10^−2	1.41⋅10^−1	0.99	6.54⋅10^−3	1.07⋅10^−2
30				1.35⋅10^−4	1.78⋅10^−4		1.37⋅10^−3	1.82⋅10^−3		1.84⋅10^−4	2.53⋅10^−4
50				1.96⋅10^−5	2.47⋅10^−5		2.45⋅10^−4	3.14⋅10^−4		4.30⋅10^−5	5.71⋅10^−5
70				3.41⋅10^−6	4.20⋅10^−6		4.86⋅10^−5	6.10⋅10^−5		7.03⋅10^−6	9.16⋅10^−6
10	4	3	0.1	4.54⋅10^−3	1.67⋅10^−2	0.5	2.36⋅10^−2	8.98⋅10^−2	0.99	1.43⋅10^−3	5.85⋅10^−3
30				2.86⋅10^−6	8.06⋅10^−6		2.73⋅10^−5	8.33⋅10^−5		2.96⋅10^−6	1.03⋅10^−5
50				8.61⋅10^−8	2.37⋅10^−7		1.22⋅10^−6	3.54⋅10^−6		1.72⋅10^−7	5.72⋅10^−7
70				1.81⋅10^−8	5.12⋅10^−8		2.10⋅10^−7	6.53⋅10^−7		3.30⋅10^−8	1.19⋅10^−7
10	6	4	0.1	4.92⋅10^−3	2.27⋅10^−2	0.5	2.77⋅10^−2	1.33⋅10^−1	0.99	8.80⋅10^−3	1.67⋅10^−3
30				2.83⋅10^−6	1.01⋅10^−5		2.71⋅10^−5	1.06⋅10^−4		3.00⋅10^−6	1.35⋅10^−5
50				7.88⋅10^−8	2.73⋅10^−7		5.48⋅10^−7	2.19⋅10^−6		6.94⋅10^−8	3.25⋅10^−7
70				1.49⋅10^−8	5.30⋅10^−8		1.74⋅10^−7	6.87⋅10^−7		2.72⋅10^−8	1.26⋅10^−7