Theory and Modern Applications
Table 3 Computational time, maximum norm of the errors and the order of convergence by using Difference Problem 1 for the Example 1 and Example 2 on a parallelogram
From: Hexagonal grid approximation of the solution of the heat equation on special polygons
(h,τ) | \(\mathrm{CT}^{Ex1}\) | \(\Vert \varepsilon _{\mathrm{Par}}^{Ex1(h,\tau )} \Vert _{\infty }\) | \({}_{2}\Re _{\mathrm{Par}}^{Ex1}\) | \(\mathrm{CT}^{Ex2}\) | \(\Vert \varepsilon _{\mathrm{Par}}^{Ex2(h,\tau )} \Vert _{\infty }\) | \({}_{2}\Re _{\mathrm{Par}}^{Ex2}\) |
|---|---|---|---|---|---|---|
(2−3,2−8) | neg | 6.63405E-5 | 1.980 | neg | 1.31396E-2 | 1.992 |
(2−4,2−9) | 0.02 | 1.68183E-5 | 1.997 | 0.02 | 3.30422E-3 | 2.002 |
(2−5,2−10) | 0.03 | 4.21369E-6 | 2.000 | 0.05 | 8.24839E-4 | 2.001 |
(2−6,2−11) | 0.16 | 1.05350E-6 | 2.001 | 0.19 | 2.06009E-4 | 2.002 |
(2−7,2−12) | 1.58 | 2.63097E-7 | 2.002 | 1.63 | 5.14365E-5 | 2.002 |
(2−8,2−13) | 3.69 | 6.56738E-8 | 4.62 | 1.28391E-5 |