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Theory and Modern Applications

Table 6 Mean absolute deviation of different methods for second-order ODEs

From: A novel improved extreme learning machine algorithm in solving ordinary differential equations by Legendre neural network methods

ODEs

SM

DM

CNN (IELM)

LNN

Example 5

3.630769e–10

1.838151e–05

0.004091

1.911390e–13

Example 6

5.590491e–11

1.046468e–05

0.004280

6.852182e–12

Example 7

1.794887e–11

1.282581e–06

0.003461

1.783986e–13

Example 8

1.110794e–09

1.439213e–05

0.001528

8.837987e–11