Research Article
Design Feed Forward Neural Network to Solve Singular Boundary Value Problems
Table 1
Analytic and neural solutions of Example
1.
| Input | Analytic solution |
Out of suggested FFNN for different training algorithms | | | Trainlm | Trainbfg | Trainbr |
| 0.0 | 1 | 1 | 1.00026931058869 | 1.00000028044679 | 0.1 | 0.995004165278026 | 0.994992000703617 | 0.995004165151447 | 0.995003016942414 | 0.2 | 0.980066577841242 | 0.980066577841242 | 0.980038331595444 | 0.980068202697384 | 0.3 | 0.955336489125606 | 0.955336489125606 | 0.955326539544390 | 0.955327719921018 | 0.4 | 0.921060994002885 | 0.921060994002885 | 0.921060993873107 | 0.921057767471849 | 0.5 | 0.877582561890373 | 0.877582561890373 | 0.877583333411869 | 0.877587507015204 | 0.6 | 0.825335614909678 | 0.825335614909678 | 0.825335614867241 | 0.825332390929038 | 0.7 | 0.764842187284489 | 0.764838404395133 | 0.764842187227892 | 0.764831348535762 | 0.8 | 0.696706709347165 | 0.696656420761032 | 0.696706709263878 | 0.696708274506624 | 0.9 | 0.621609968270664 | 0.621454965504409 | 0.621609968278774 | 0.621608898908218 | 1.0 | 0.540302305868140 | 0.540302305868140 | 0.540302305877365 | 0.540302558954826 |
|
|