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

Table 3

Maximum absolute error for 𝛾=1/100, with various choices of 𝑁, for Example 5 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	1	1.5	7.97⋅10^−6	2.47⋅10^−5	0.9	7.28⋅10^−7	1.40⋅10^−6	0.5	1.10⋅10^−6	1.89⋅10^−6
30				1.38⋅10^−6	3.81⋅10^−6		7.11⋅10^−8	1.21⋅10^−7		7.39⋅10^−8	1.11⋅10^−7
50				4.02⋅10^−7	1.09⋅10^−6		1.51⋅10^−8	2.49⋅10^−8		1.29⋅10^−8	1.88⋅10^−8
70				2.51⋅10^−7	6.64⋅10^−7		3.79⋅10^−9	6.15⋅10^−9		5.86⋅10^−9	8.41⋅10^−9
10	2	2	1.5	5.39⋅10^−6	4.44⋅10^−5	0.9	6.29⋅10^−7	2.78⋅10^−6	0.5	9.85⋅10^−7	3.54⋅10^−6
30				1.33⋅10^−7	9.33⋅10^−7		8.65⋅10^−9	3.20⋅10^−8		9.31⋅10^−9	2.77⋅10^−8
50				4.26⋅10^−8	3.00⋅10^−7		2.00⋅10^−9	7.37⋅10^−9		1.71⋅10^−9	5.06⋅10^−9
70				1.78⋅10^−8	1.22⋅10^−7		7.56⋅10^−10	2.72⋅10^−9		5.28⋅10^−10	1.52⋅10^−9
10	5	3	1.5	1.19⋅10^−6	1.87⋅10^−5	0.9	1.67⋅10^−7	1.34⋅10^−6	0.5	2.94⋅10^−7	1.87⋅10^−6
30				2.25⋅10^−8	3.48⋅10^−7		1.58⋅10^−9	1.09⋅10^−8		1.76⋅10^−9	1.02⋅10^−8
50				1.28⋅10^−8	1.92⋅10^−7		5.85⋅10^−10	4.27⋅10^−9		5.97⋅10^−10	3.33⋅10^−9
70				8.52⋅10^−9	1.26⋅10^−7		3.21⋅10^−10	2.30⋅10^−9		2.81⋅10^−10	1.53⋅10^−9