Advances in Artificial Neural Systems / 2013 / Article / Tab 1

Research Article

Comparison of Artificial Neural Network Architecture in Solving Ordinary Differential Equations

Table 1

Analytical and neural solutions with arbitrary and regression based weights (Example 1).

Input dataAnalyticalNeural results
  
(four nodes)
  
(four nodes)
  
(five nodes)
  
(five nodes)
  
(six nodes)
Deviation%   
(six nodes)
Deviation%

01.00001.00001.00001.00001.00001.00000.001.00000.00
0.050.95361.00150.99981.00020.97680.98863.670.96771.47
0.100.91370.98670.95930.94980.92030.90840.580.91590.24
0.150.87980.92480.89860.89060.88020.89061.220.88150.19
0.200.85140.90880.88690.85640.86660.85870.850.85310.19
0.250.82830.87490.86300.85090.84940.83090.310.82640.22
0.300.81040.85160.84810.82130.92890.80131.120.81140.12
0.350.79780.82640.80300.81860.80510.79990.260.79530.31
0.400.79050.81370.79100.81080.80830.79180.160.78940.13
0.450.78890.79510.79080.80280.79480.78280.770.78450.55
0.500.79310.80740.80630.80070.79600.80471.460.79570.32
0.550.80330.81770.81370.82760.81020.80760.530.80410.09
0.600.82000. 82110.81900.83620.82460.81520.580.82040.04
0.650.84310.86170.85780.85190.85010.83191.320.83990.37
0.700.87310.88960.87550.86850.87940.85921.590.87110.22
0.750.91010.92810.92310.92290.91390.91290.310.91510.54
0.800.95410.97770.96130.98970.96030.97552.240.95550.14
0.851.00531.08190.99300.99561. 00581.00560.030.99481.04
0.901.06371.08491.10201.07141.06631.07140.721.06620.23
0.951.12931.20111.13001.15881.13071.12810.111.13060.11
1.001.20221.26901.21951.28061.21391.21080.711.20580.29

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