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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