Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

Table 6

Accuracy of solutions for Example 2.

The error 𝐸(𝑥)=|𝑦𝑡(𝑥)−𝑦𝑎(𝑥)| where 𝑦𝑡(𝑥) computed by the following training algorithm
Trainlm	Trainbfg	trainbr
0	2.19047002758543𝑒−13	8.49512027389920𝑒−09
2.59583678221542𝑒−05	8.43198383004840𝑒−06	1.23563152347739𝑒−05
9.84181703400644𝑒−06	2.84760554247754𝑒−06	2.52316951554477𝑒−07
0	6.74571509762245𝑒−13	9.09160424944489𝑒−07
0	1.55675472512939𝑒−12	1.20527650837587𝑒−06
0	1.16662235427611𝑒−12	1.93011959059852𝑒−06
2.22044604925031𝑒−16	4.86721773995669𝑒−13	2.11336051969546𝑒−06
5.72295631107167𝑒−06	1.71480126542889𝑒−07	3.07126269616376𝑒−06
0	5.72875080706581𝑒−14	2.20510526371953𝑒−06
4.99376847331590𝑒−05	1.19798370104007𝑒−05	8.49031051686211𝑒−07
0	1.51878509768721𝑒−13	1.41819320731429𝑒−07