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Theory and Modern Applications

Table 3 Comparison between approximate series solutions and absolute errors obtained by DTM [5] and the proposed technique LeNN-GNDO-SQP for different cases of problem 1

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

Case I

Case II

Case III

Case IV

DTM [5]

LeNN-GNDO-SQP

DTM [5]

LeNN-GNDO-SQP

0.0

0

0.00000176

0.00000136

0.00000289

0.00000113

0.00E+00

1.14E−08

1.46E−07

1.82E−06

4.19E−06

0.1

0.029550

0.02956135

0.03132029

0.03570346

0.04582241

7.60E−05

2.52E−07

6.09E−06

9.31E−05

2.45E−04

0.2

0.109271

0.10920960

0.11491897

0.12292936

0.13638881

1.71E−04

7.49E−07

3.65E−05

5.60E−04

1.72E−03

0.3

0.225724

0.22579397

0.23590901

0.24791745

0.26469397

1.73E−04

1.75E−07

3.35E−05

5.38E−04

2.23E−03

0.4

0.365524

0.36554203

0.37940757

0.39428366

0.41286626

7.30E−05

1.90E−07

1.52E−06

1.14E−05

2.88E−05

0.5

0.515532

0.51563973

0.53111109

0.54666803

0.56465531

7.70E−05

2.19E−07

3.64E−05

4.36E−04

1.09E−03

0.6

0.663060

0.66301561

0.67774161

0.69142917

0.70634372

2.11E−04

3.71E−08

1.28E−06

1.73E−05

2.85E−04

0.7

0.796061

0.79612341

0.80740818

0.81709777

0.82717307

2.67E−04

2.26E−07

3.15E−05

2.62E−04

2.84E−04

0.8

0.903288

0.90323062

0.90982011

0.91450894

0.91924769

2.20E−04

7.90E−08

3.34E−05

2.39E−04

4.61E−04

0.9

0.974391

0.97439092

0.97633288

0.97664600

0.97707676

9.40E−05

4.53E−09

5.57E−06

3.12E−05

7.43E−05

1.0

1

0.99999999

0.99999987

0.99999944

0.99999975

0.00E+00

5.62E−12

1.39E−07

1.10E−06

9.91E−07