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Theory and Modern Applications

Table 9 Statistical analysis of absolute errors in term of minimum, mean and standard deviation for different cases of problem 2

From: Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel

η

Case I

Case II

Case III

Case IV

Min

Mean

Std

Min

Mean

Std

Min

Mean

Std

Min

Mean

Std

0.00

1.40E−11

6.15E−08

2.74E−07

7.11E−13

1.14E−07

2.83E−07

2.21E−11

2.29E−07

1.74E−06

9.39E−14

3.09E−07

9.46E−07

0.50

1.39E−10

1.30E−07

2.10E−07

1.46E−10

4.30E−06

7.80E−06

5.55E−13

3.57E−05

8.87E−05

1.34E−07

2.72E−04

7.16E−04

0.10

3.89E−10

1.74E−07

5.69E−07

1.68E−10

1.36E−06

2.77E−06

2.64E−11

4.03E−06

2.38E−05

8.09E−11

7.18E−06

2.49E−05

0.15

4.04E−12

1.04E−07

4.68E−07

2.34E−10

2.24E−07

3.72E−07

3.62E−12

6.00E−06

1.19E−05

4.22E−09

3.97E−05

1.04E−04

0.20

9.24E−12

5.93E−08

1.45E−07

2.25E−10

1.42E−06

2.43E−06

5.55E−12

9.87E−06

3.18E−05

1.81E−09

2.75E−05

7.80E−05

0.25

3.83E−12

5.08E−08

7.07E−08

6.58E−12

1.20E−06

2.26E−06

2.49E−10

4.19E−06

2.35E−05

1.01E−08

5.40E−06

1.09E−05

0.30

8.59E−13

6.16E−08

1.39E−07

2.93E−12

2.80E−07

9.80E−07

7.22E−10

3.75E−06

8.94E−06

9.12E−10

1.92E−05

5.39E−05

0.35

8.77E−13

8.49E−08

3.46E−07

7.81E−11

3.93E−07

6.63E−07

1.67E−12

6.38E−06

1.43E−05

1.95E−10

1.95E−05

3.95E−05

0.40

5.53E−12

1.05E−07

4.14E−07

1.95E−11

1.00E−06

1.54E−06

2.70E−11

6.29E−06

2.59E−05

1.05E−09

7.77E−06

1.17E−05

0.45

1.13E−12

9.89E−08

2.75E−07

2.44E−12

8.79E−07

1.42E−06

1.83E−11

5.41E−06

1.92E−05

2.46E−11

1.30E−05

4.77E−05

0.50

1.13E−11

6.38E−08

9.54E−08

5.31E−12

3.14E−07

9.59E−07

3.09E−12

5.07E−06

1.29E−05

1.83E−12

2.32E−05

5.06E−05

0.55

3.69E−13

3.34E−08

4.73E−08

1.64E−10

3.62E−07

8.21E−07

1.12E−10

4.98E−06

1.14E−05

1.52E−09

1.48E−05

2.18E−05

0.60

7.57E−16

4.92E−08

1.61E−07

3.30E−11

8.79E−07

1.31E−06

4.15E−11

6.92E−06

2.62E−05

1.00E−10

1.01E−05

3.64E−05

0.65

2.71E−11

1.09E−07

3.84E−07

1.15E−11

8.00E−07

1.09E−06

7.51E−11

8.68E−06

2.21E−05

3.95E−12

2.91E−05

8.70E−05

0.70

7.53E−11

1.52E−07

4.27E−07

5.28E−15

2.51E−07

6.59E−07

2.41E−09

5.23E−06

1.33E−05

2.86E−10

2.90E−05

4.57E−05

0.75

2.88E−12

1.14E−07

2.23E−07

7.83E−12

5.42E−07

1.14E−06

4.65E−13

4.18E−06

1.40E−05

5.54E−09

7.05E−06

1.44E−05

0.80

2.25E−13

3.10E−08

4.12E−08

5.49E−13

1.27E−06

1.84E−06

2.98E−09

1.41E−05

3.77E−05

4.55E−09

4.36E−05

1.24E−04

0.85

1.20E−12

6.03E−08

2.00E−07

5.82E−12

5.33E−07

6.59E−07

5.66E−09

1.12E−05

2.27E−05

2.63E−09

5.77E−05

9.25E−05

0.90

1.37E−11

2.61E−07

6.87E−07

1.29E−10

6.74E−07

1.17E−06

5.03E−10

5.43E−06

1.73E−05

2.11E−09

1.14E−05

3.96E−05

0.95

7.01E−13

2.70E−07

5.49E−07

1.38E−09

4.04E−06

5.27E−06

6.65E−08

7.40E−05

1.41E−04

3.26E−07

3.51E−04

5.19E−04

1.00

1.65E−13

4.47E−08

1.25E−07

4.10E−12

3.90E−08

7.36E−08

1.52E−12

2.89E−07

9.33E−07

9.68E−13

4.53E−07

1.64E−06