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Table 10 Exact and LNN neural network results

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

Input points \(x_{k}\) Exact results LNN results Absolute error
0 1 1 0
0.1 0.9966699984131 0.9966699984129 1.8e–13
0.2 0.9867198985254 0.9867198985252 2.2e–13
0.3 0.9702688457452 0.9702688457450 2.3e–13
0.4 0.9475135272247 0.9475135272245 2.3e–13
0.5 0.9187253698655 0.9187253698653 2.3e–13
0.6 0.8842466786034 0.8842466786032 2.2e–13
0.7 0.8444857748514 0.8444857748511 2.2e–13
0.8 0.7999112103978 0.7999112103976 2.1e–13
0.9 0.7510451462491 0.7510451462489 2.0e–13
1 0.6984559986366 0.6984559986364 1.8e–13