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Theory and Modern Applications

Table 7 Solution at some points on \(t=1\), and the order of convergence by using Difference Problem 1 for the Example 3

From: Hexagonal grid approximation of the solution of the heat equation on special polygons

P

\(u_{2^{-4},2^{-9}} ( P ) \)

\(u_{2^{-5},2^{-10}} ( P ) \)

\(u_{2^{-6},2^{-11}} ( P ) \)

\({}_{2}\Re _{\mathrm{Rec}}^{Ex3} ( P ) \)

\(( 0.125,\frac{\sqrt{3}}{16},1 ) \)

−4.58409E-6

−1.03024E-6

−1.4070E-7

1.998

\(( 0.25,\frac{\sqrt{3}}{16},1 ) \)

−1.80759E-6

6.79206E-6

8.94335E-6

1.999

\(( 0.375,\frac{\sqrt{3}}{16},1 ) \)

7.67420E-5

9.37204E-5

9.79542E-5

2.004

\(( 0.5,\frac{\sqrt{3}}{16},1 ) \)

4.35627E-4

4.64628E-4

4.71821E-4

2.011

\(( 0.625,\frac{\sqrt{3}}{16},1 ) \)

1.36634E-3

1.40760E-3

1.41775E-3

2.023

\(( 0.75,\frac{\sqrt{3}}{16},1 ) \)

2.87207E-3

2.91762E-3

2.92870E-3

2.039

\(( 0.875,\frac{\sqrt{3}}{16},1 ) \)

3.75741E-3

3.78878E-3

3.79627E-3

2.066