Solution of the Porous Media Equation by a Compact Finite Difference Method

Table 6

Convergence rate (CR) of the present scheme: Comparisons on various values of ℎ,𝑡 and Δ𝑡 for 3.5.

𝑡=0.0001,Δ𝑡=1.0E-06			𝑡=0.0003,Δ𝑡=1.0E-06			𝑡=0.0003,Δ𝑡=1.0E-05
ℎ	Average absolute error	CR	ℎ	Average absolute error	CR	ℎ	Average absolute error	CR
1/10	5.84E-09		1/18	6.82E-10		1/18	8.95E-10
1/15	6.86E-10	5.28	1/20	3.84E-10	5.45	1/20	5.06E-10	5.42
1/20	1.48E-10	5.34	1/22	2.27E-10	5.54	1/22	2.99E-10	5.51
1/25	4.36E-11	5.46	1/24	1.39E-10	5.62	1/24	1.84E-10	5.60
1/30	1.58E-11	5.57	1/26	8.80E-11	5.71	1/26	1.17E-10	5.68
1/35	6.57E-12	5.69	1/28	5.72E-11	5.80	1/28	7.60E-11	5.77
1/40	3.03E-12	5.80	1/30	3.81E-11	5.89	1/30	5.07E-11	5.86
1/45	1.51E-12	5.91	1/32	2.59E-11	5.98	1/32	3.45E-11	5.95
1/50	8.02E-13	6.02	1/34	1.79E-11	6.07	1/34	2.39E-11	6.05
1/55	4.47E-13	6.14	1/36	1.26E-11	6.16	1/36	1.68E-11	6.15