Using Feed Forward Neural Network to Solve Eigenvalue Problems

Table 5

Analytic and neural solution of Example 2.

Input	Analytic solution	Output of suggested FFNN 𝑦𝑡(𝑥) for different training algorithms
𝑥	𝑦𝑎(𝑥)	Trainlm	Trainbfg	Trainbr
0.0	1	1.000000000000000	0.999999791497422	1.000000531336361
0.1	1.000100005000167	1.000144087759814	1.000100368418017	1.000097184294931
0.2	1.001601280682940	1.001601280682940	1.001498511767109	1.001607051239879
0.3	1.008132893753152	1.008132893753152	1.008132867669427	1.008128167440348
0.4	1.025930494190382	1.025930494190382	1.026019395339251	1.025927732110325
0.5	1.064494458917860	1.064590790583371	1.064494437575892	1.064506007546008
0.6	1.138372943065416	1.138372943065416	1.138272638536007	1.138359307576485
0.7	1.271376281592894	1.269464922443141	1.271376301269824	1.271384988973427
0.8	1.506215178528160	1.500405060697450	1.506214213098092	1.506211973532767
0.9	1.927261339283878	1.927261339283878	1.927192081328471	1.927261991541353
1.0	2.718281828459046	2.718281828459046	2.718280402057775	2.718281767743469