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Theory and Modern Applications

Table 2 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 trapezoid

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

(h,τ)

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

\(\Vert \varepsilon_{\mathrm{Tra}}^{Ex1(h,\tau )} \Vert _{\infty }\)

\({}_{2}\Re _{\mathrm{Tra}}^{Ex1}\)

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

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

\({}_{2}\Re _{\mathrm{Tra}}^{Ex2}\)

(2−3,2−8)

neg

7.47982E-5

1.971

neg

1.40022E-2

1.989

(2−4,2−9)

0.02

1.90801E-5

1.999

0.02

3.52824E-3

2.001

(2−5,2−10)

0.05

4.77247E-6

1.999

0.05

8.81499E-4

2.002

(2−6,2−11)

0.20

1.19371E-6

2.000

0.25

2.20072E-4

2.002

(2−7,2−12)

2.20

2.98412E-7

2.000

2,33

5.49334E-5

2.002

(2−8,2−13)

4.41

7.45783E-8

 

4.88

1.37127E-5