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Theory and Modern Applications

Table 6 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 parallelogram

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

(h,τ)

\(\mathrm{CT}^{Ex1}\)

\(\Vert \varepsilon _{\mathrm{Par}}^{Ex1(h,\tau )} \Vert _{\infty }\)

\({}_{4}\Re _{\mathrm{Par}}^{Ex1}\)

\(\mathrm{CT}^{Ex2}\)

\(\Vert \varepsilon _{\mathrm{Par}}^{Ex2(h,\tau )} \Vert _{\infty }\)

\({}_{4}\Re _{\mathrm{Par}}^{Ex2}\)

(2−4,2−6)

neg

5.25821E-4

3.963

0.02

4.35263E-3

3.981

(2−5,2−10)

0.03

3.37165E-5

3.998

0.06

2.75544E-4

3.999

(2−6,2−14)

0.17

2.11066E-6

4.000

0.30

1.72353E-5

4.000

(2−7,2−18)

1.19

1.31906E-7

4.000

1.81

1.07708E-6

4.000

(2−8,2−22)

3.98

8.24304E-9

 

4.78

6.73085E-8