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Theory and Modern Applications

Table 4 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 rectangle

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

(h,τ)

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

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

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

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

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

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

(2−4,2−6)

neg

4.95534E-4

3.965

0.02

4.66691E-3

3.981

(2−5,2−10)

0.03

3.17373E-5

3.997

0.08

2.95518E-4

3.999

(2−6,2−14)

0.14

1.98759E-6

3.999

0.34

1.84851E-5

4.000

(2−7,2−18)

1.13

1.24291E-7

4.000

1.88

1.15518E-6

4.000

(2−8,2−22)

3.24

7.76738E-9

 

3.98

7.21861E-8