Research Article
Design Feed Forward Neural Network to Solve Singular Boundary Value Problems
Table 5
Analytic and neural solutions of Example
2.
| Input | Analytic solution |
Out of suggested FFNN for different training algorithms | | | Trainlm | Trainbfg | Trainbr |
| 0.0 | 1 | 1 | 0.999999999999781 | 0.999999991504880 | 0.1 | 1.10517091807565 | 1.10514495970783 | 1.10517935005948 | 1.10518327439088 | 0.2 | 1.22140275816017 | 1.22139291634314 | 1.22140560576571 | 1.22140301047712 | 0.3 | 1.34985880757600 | 1.34985880757600 | 1.34985880757533 | 1.34985789841558 | 0.4 | 1.49182469764127 | 1.49182469764127 | 1.49182469764283 | 1.49182590291778 | 0.5 | 1.64872127070013 | 1.64872127070013 | 1.64872127069896 | 1.64871934058054 | 0.6 | 1.82211880039051 | 1.82211880039051 | 1.82211880039100 | 1.82211668702999 | 0.7 | 2.01375270747048 | 2.01374698451417 | 2.01375253599035 | 2.01375577873317 | 0.8 | 2.22554092849247 | 2.22554092849247 | 2.22554092849241 | 2.22553872338720 | 0.9 | 2.45960311115695 | 2.45965304884168 | 2.45961509099396 | 2.45960396018800 | 1.0 | 2.71828182845905 | 2.71828182845905 | 2.71828182845889 | 2.71828168663973 |
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