A Banded Preconditioning Iteration Method for Time-Space Fractional Advection-Diffusion Equations

Table 1

Numerical results of the tested methods for and .

		S-GMRES		T-GMRES		R-GMRES		(16)-GMRES		(4)-GMRES
		IT	CPU	IT	CPU	IT	CPU	IT	CPU	IT	CPU
1.3		18	0.18	22	0.24	18	0.15	8	0.07	5	0.05
		20	0.51	26	0.58	19	0.43	8	0.18	5	0.12
		21	1.60	30	2.23	21	1.61	8	0.63	5	0.53
		22	9.12	35	14.14	22	9.14	8	3.02	5	2.33
		23	51.10	39	83.54	23	51.21	8	18.57	5	12.44
		23	306.29	44	560.60	23	307.80	8	110.39	5	75.95
		—	—	—	—	—	—	8	741.27	5	495.16
1.6		11	0.09	18	0.17	11	0.11	8	0.08	4	0.06
		12	0.28	22	0.46	12	0.28	8	0.17	4	0.11
		12	0.97	26	1.93	12	0.97	8	0.63	4	0.43
		12	5.26	30	12.11	12	5.30	8	3.46	4	2.32
		12	28.88	36	77.01	12	28.60	8	18.7	4	12.4
		12	169.48	43	547.79	12	169.37	8	109.46	4	73.25
		12	1153.13	—	—	12	1157.55	8	742.61	4	496.21
1.9		8	0.08	18	0.15	8	0.08	6	0.06	3	0.04
		8	0.19	22	0.46	8	0.19	6	0.14	3	0.1
		8	0.71	27	2.00	8	0.70	6	0.49	3	0.36
		8	3.79	34	13.58	8	3.81	6	2.71	3	1.93
		8	21.18	44	93.08	8	20.57	6	14.45	3	10.36
		8	121.58	57	717.37	8	121.41	6	85.41	3	61.08
		7	745.34	—	—	7	742.52	6	578.17	3	413.03