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

Table 2

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	0.16	22	0.20	18	0.16	8	0.07	5	0.05
		20	0.43	26	0.55	19	0.40	8	0.17	5	0.12
		21	1.59	30	2.22	21	1.60	8	0.63	5	0.43
		22	9.12	35	14.03	22	9.11	8	3.04	5	2.32
		23	51.60	39	83.07	23	51.10	8	18.52	5	12.83
		23	302.65	44	559.36	23	308.72	8	109.32	5	73.38
		—	—	—	—	—	—	8	736.5	5	493
1.6		11	0.10	18	0.15	11	0.10	8	0.07	4	0.04
		12	0.27	22	0.46	12	0.37	8	0.17	4	0.27
		12	0.96	26	1.92	12	0.97	8	0.62	4	0.44
		12	5.30	30	12.02	12	5.30	8	3.42	4	2.32
		12	28.66	36	77.11	12	30.14	8	18.55	4	12.38
		12	169.48	43	547.61	12	170.06	8	109.37	4	73.19
		12	1146.07	—	—	12	1146.50	8	738.33	4	494.49
1.9		8	0.07	18	0.15	8	0.07	6	0.06	3	0.04
		8	0.19	22	0.46	8	0.19	6	0.14	3	0.1
		8	0.70	27	2.00	8	0.72	6	0.49	3	0.35
		8	4.22	34	13.76	8	3.82	6	2.7	3	1.94
		8	20.79	44	93.85	8	20.52	6	14.44	3	10.39
		8	121.68	57	717.90	8	121.76	6	85.35	3	61.15
		7	740.29	—	—	7	742.03	6	576.51	3	411.58