Theory and Modern Applications
Table 8 Solution at some points on \(t=1\), and the order of convergence by using Difference Problem 2 for the Example 3
From: Hexagonal grid approximation of the solution of the heat equation on special polygons
P | \(u_{2^{-4},2^{-6}} ( P ) \) | \(u_{2^{-5},2^{-10}} ( P ) \) | \(u_{2^{-6},2^{-14}} ( P ) \) | \({}_{4}\Re _{\mathrm{Rec}}^{Ex3} ( P ) \) |
|---|---|---|---|---|
\(( 0.125,\frac{\sqrt{3}}{16},1 ) \) | 1.21289E-7 | 1.53563E-7 | 1.55701E-7 | 3.916 |
\(( 0.25,\frac{\sqrt{3}}{16},1 ) \) | 9.57959E-6 | 9.6543E-6 | 9.65919E-6 | 3.933 |
\(( 0.375,\frac{\sqrt{3}}{16},1 ) \) | 9.91752E-5 | 9.93431E-5 | 9.93539E-5 | 3.958 |
\(( 0.5,\frac{\sqrt{3}}{16},1 ) \) | 4.73794E-4 | 4.74143E-4 | 4.74165E-4 | 3.988 |
\(( 0.625,\frac{\sqrt{3}}{16},1 ) \) | 1.42033E-3 | 1.42094E-3 | 1.42098E-3 | 3.931 |
\(( 0.75,\frac{\sqrt{3}}{16},1 ) \) | 2.93121E-3 | 2.93202E-3 | 2.93207E-3 | 4.018 |
\(( 0.875,\frac{\sqrt{3}}{16},1 ) \) | 3.79768E-3 | 3.79832E-3 | 3.79836E-3 | 4.000 |