Mathematical Problems in Engineering / 2009 / Article / Tab 6

Research Article

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 , 𝑡 and Δ 𝑡 for 3.5.

𝑡 = 0 . 0 0 0 1 , Δ 𝑡 = 1 . 0 E - 0 6 𝑡 = 0 . 0 0 0 3 , Δ 𝑡 = 1 . 0 E - 0 6 𝑡 = 0 . 0 0 0 3 , Δ 𝑡 = 1 . 0 E - 0 5

Average absolute errorCR Average absolute errorCR Average absolute errorCR

1 / 1 0 5.84E-09 1 / 1 8 6.82E-10 1 / 1 8 8.95E-10
1 / 1 5 6.86E-105.28 1 / 2 0 3.84E-105.45 1 / 2 0 5.06E-105.42
1 / 2 0 1.48E-105.34 1 / 2 2 2.27E-105.54 1 / 2 2 2.99E-105.51
1 / 2 5 4.36E-115.46 1 / 2 4 1.39E-105.62 1 / 2 4 1.84E-105.60
1 / 3 0 1.58E-115.57 1 / 2 6 8.80E-115.71 1 / 2 6 1.17E-105.68
1 / 3 5 6.57E-125.69 1 / 2 8 5.72E-115.80 1 / 2 8 7.60E-115.77
1 / 4 0 3.03E-125.80 1 / 3 0 3.81E-115.89 1 / 3 0 5.07E-115.86
1 / 4 5 1.51E-125.91 1 / 3 2 2.59E-115.98 1 / 3 2 3.45E-115.95
1 / 5 0 8.02E-136.02 1 / 3 4 1.79E-116.07 1 / 3 4 2.39E-116.05
1 / 5 5 4.47E-136.14 1 / 3 6 1.26E-116.16 1 / 3 6 1.68E-116.15

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