Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

Table 2

Accuracy of solution for Example 1.

The error 𝐸(𝑥)=|𝑦𝑡(𝑥)−𝑦𝑎(𝑥)| where 𝑦𝑡(𝑥) computed by the following training algorithm
Trainlm	Trainbfg	Trainbr
0	0.000269310588686622	2.80446790679179𝑒−07
1.21645744084464𝑒−05	1.26578747483563𝑒−10	1.14833561148942𝑒−06
0	2.82462457977806𝑒−05	1.62485614274566𝑒−06
0	9.94958121636191𝑒−06	8.76920458825481𝑒−06
0	1.29778077173626𝑒−10	3.22653103579373𝑒−06
0	7.71521496467642𝑒−07	4.94512483140142𝑒−06
0	4.24377200047843𝑒−11	3.22398064012130𝑒−06
3.78288935598548𝑒−06	5.65963942378289𝑒−11	1.08387487263162𝑒−05
5.02885861338731𝑒−05	8.32875990397497𝑒−11	1.56515945903823𝑒−06
0.000155002766255130	8.10940203876953𝑒−12	1.06936244681499𝑒−06
0	9.22539822312274𝑒−12	2.53086685830795𝑒−07