Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method

Table 3

Comparison between numerical solutions and the exact solution.

𝑥	MOCS	MOCG	CBSG	FEMLSF	FEMQSF	TC	TG	CD6		Exact
	[28]	[11]	[31]	[34]	[34]	[32]	[32]	Δ𝑡=10 s	Δ𝑡=1 s
0	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
18	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
19	1.000	0.999	1.000	1.000	1.000	0.999	0.999	0.999	0.999	0.999
20	1.000	0.998	0.999	0.999	1.000	0.999	0.998	0.998	0.998	0.998
21	1.000	0.996	0.996	0.997	0.999	0.999	0.996	0.996	0.996	0.996
22	1.000	0.990	0.991	0.993	0.996	0.998	0.991	0.992	0.991	0.991
23	1.000	0.978	0.981	0.985	0.989	0.994	0.980	0.982	0.982	0.982
24	1.000	0.957	0.961	0.970	0.974	0.987	0.960	0.965	0.964	0.964
25	1.000	0.922	0.927	0.943	0.946	0.972	0.926	0.936	0.935	0.934
26	0.996	0.870	0.874	0.902	0.900	0.945	0.874	0.891	0.889	0.889
27	1.013	0.799	0.800	0.842	0.832	0.902	0.800	0.827	0.824	0.823
28	1.047	0.708	0.706	0.763	0.743	0.838	0.705	0.743	0.739	0.738
29	0.897	0.602	0.596	0.666	0.638	0.755	0.595	0.641	0.637	0.636
30	0.457	0.488	0.479	0.556	0.524	0.653	0.479	0.528	0.523	0.523
31	0.067	0.375	0.366	0.442	0.411	0.541	0.366	0.413	0.408	0.408
32	−0.036	0.272	0.265	0.332	0.306	0.427	0.264	0.306	0.301	0.301
33	−0.010	0.185	0.181	0.235	0.218	0.320	0.181	0.212	0.208	0.208
34	0.002	0.118	0.118	0.156	0.147	0.227	0.117	0.138	0.135	0.135
35	0.000	0.070	0.072	0.096	0.095	0.152	0.072	0.084	0.082	0.082
36	0.000	0.038	0.042	0.055	0.058	0.096	0.041	0.048	0.047	0.046
37	0.000	0.020	0.023	0.030	0.034	0.057	0.023	0.025	0.025	0.024
38	0.000	0.009	0.012	0.015	0.019	0.032	0.012	0.012	0.012	0.012
39	0.000	0.004	0.006	0.007	0.010	0.017	0.006	0.006	0.005	0.005
40	0.000	0.002	0.003	0.003	0.005	0.008	0.002	0.002	0.002	0.002
41	0.000	0.001	0.001	0.001	0.003	0.004	0.001	0.001	0.001	0.001
42	0.000	0.000	0.001	0.000	0.001	0.001	0.000	0.000	0.000	0.000