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Theory and Modern Applications

Table 3 Mean absolute deviation of different methods for first-order ODEs

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

ODEs

EM

Suen-R-K3

R-K4

CNN(GD)

CNN(IELM)

LNN

Example 1

0.009438

7.199659e–08

3.516257e–11

3.038010e–04

0.018023

6.070510e–08

Example 2

0.006143

2.556570e–08

2.508454e–11

5.306315e–04

0.010317

1.654316e–10

Example 3

0.003830

6.992166e–08

4.140991e–10

2.502357e–04

0.007621

2.191930e–08

Example 4

0.005874

4.650619e–09

2.364301e–11

2.463780e–04

0.010018

2.180179e–12