Theory and Modern Applications
Table 1 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 rectangle
From: Hexagonal grid approximation of the solution of the heat equation on special polygons
(h,τ) | \(\mathrm{CT}^{Ex1}\) | \(\Vert \varepsilon_{\mathrm{Rec}}^{Ex1(h,\tau )} \Vert _{\infty }\) | \({}_{2}\Re _{\mathrm{Rec}}^{Ex1}\) | \(\mathrm{CT}^{Ex2}\) | \(\Vert \varepsilon _{\mathrm{Rec}}^{Ex2(h,\tau )} \Vert _{\infty }\) | \({}_{2}\Re _{\mathrm{Rec}}^{Ex2}\) |
|---|---|---|---|---|---|---|
(2−3,2−8) | neg | 6.24429E-5 | 1.978 | neg | 9.35402E-3 | 1.983 |
(2−4,2−9) | 0.02 | 1.58525E-5 | 1.999 | 0.02 | 2.36716E-3 | 2.001 |
(2−5,2−10) | 0.03 | 3.96648E-6 | 1.999 | 0.03 | 5.91299E-4 | 2.002 |
(2−6,2−11) | 0.16 | 9.92099E-7 | 2.000 | 0.19 | 1.47588E-4 | 2.003 |
(2−7,2−12) | 1.52 | 2.48027E-7 | 2.000 | 1.66 | 3.68223E-5 | 2.004 |
(2−8,2−13) | 3.50 | 6.19891E-8 | 3.76 | 9.17993E-6 |