Theory and Modern Applications
Table 5 Computational time, maximum norm of the errors and the order of convergence by using Difference Problem 2 for the Example 1 and Example 2 on a trapezoid
From: Hexagonal grid approximation of the solution of the heat equation on special polygons
(h,τ) | \(\mathrm{CT}^{Ex1}\) | \(\Vert \varepsilon _{\mathrm{Tra}}^{Ex1(h,\tau )} \Vert _{\infty }\) | \({}_{4}\Re _{\mathrm{Tra}}^{Ex1}\) | \(\mathrm{CT}^{Ex2}\) | \(\Vert \varepsilon _{\mathrm{Tra}}^{Ex2(h,\tau )} \Vert _{\infty }\) | \({}_{4}\Re _{\mathrm{Tra}}^{Ex2}\) |
|---|---|---|---|---|---|---|
(2−4,2−6) | neg | 5.97349E-4 | 3.967 | 0.02 | 5.24608E-3 | 3.980 |
(2−5,2−10) | 0.03 | 3.81931E-5 | 3.997 | 0.09 | 3.32497E-4 | 3.999 |
(2−6,2−14) | 0.20 | 2.39154E-6 | 4.000 | 0.45 | 2.08008E-5 | 4.000 |
(2−7,2−18) | 1.63 | 1.49520E-7 | 4.000 | 2.61 | 1.29993E-6 | 4.000 |
(2−8,2−22) | 4.18 | 9.34338E-9 | 4.53 | 8.12356E-8 |