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Table 8 Mean absolute deviation of different methods for SODE

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

ODEs

EM

R-K4

CNN(IELM)

LNN

Example 9

\(y_{1}\)

0.018838

2.247437e–10

0.005677

2.726976e–11

\(y_{2}\)

0.046376

5.494596e–10

0.021612

4.481164e–11

Example 10

\(y_{1}\)

0.001791

1.411037e–10

0.003651

2.296702e–12

\(y_{2}\)

0.001202

1.041297e–10

0.006159

1.792269e–12