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Theory and Modern Applications

Table 1 Mean absolute deviation of test examples with different parameters

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

Example

 

m = 100

n = 10

 

n = 5

n = 8

n = 10

m = 50

m = 200

m = 500

Example 1

 

2.179822e–04

1.124613e–07

6.070510e–08

1.594745e–08

3.258493e–08

1.893462e–08

Example 2

 

2.898579e–05

8.788694e–09

1.654316e–10

2.375011e–11

8.614644e–11

5.764976e–11

Example 3

 

2.651596e–04

1.352667e–06

2.191930e–08

2.476702e–08

2.041171-08

1.950112e–08

Example 4

 

1.365455e–15

8.406017e–14

2.180178e–12

9.360722e–13

3.13950e–12

5.474343e–12

Example 5

 

4.048192e–15

1.721054e–14

1.911390e–13

1.914236e–13

2.815815e–13

3.639675e–13

Example 6

 

1.785691e–06

3.153652e–09

6.852182e–12

4.679648e–12

1.464149e–11

1.074478e–11

Example 7

 

1.535907e–05

2.385380e–11

1.783986e–13

8.363132e–14

9.388591e–14

3.149325e–13

Example 8

 

9.719036e–04

1.792439e–08

8.837987e–11

1.108446e–10

9.767964e–11

1.867956e–10

Example 9

\(y_{1}\)

1.011548e–04

1.198037e–08

2.726976e–11

4.126236e–11

3.043601e–11

2.383795e–11

\(y_{2}\)

1.696858e–04

2.137740e–08

4.481164e–11

1.15183e–10

4.740707e–11

1.311124e–11

Example 10

\(y_{1}\)

4.814629e–07

7.071364e–12

2.296702e–12

2.432451e–12

2.747277e–12

1.456190e–12

\(y_{2}\)

2.391016e–07

3.228814e–11

1.792269e–12

8.192227e–13

6.997846e–12

5.358554e–12

Example 11

 

5.861896e–02

2.837823e–03

1.038392e–02

2.361003e–02

1.044330e–02

1.047949e–02