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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Execution time 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

1.4122

4.3523

5.7430

57.2749

0.0311

0.0056

Example 2

1.4694

4.1127

5.8199

3.6168

0.0315

0.0106

Example 3

1.3024

3.9871

5.2435

75.1474

0.0268

0.0063

Example 4

1.2431

3.9994

5.3399

46.1268

0.0272

0.0043

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