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Table 17 Problem 7 : MAEs and RMSEs using ( 2.7a )-( 2.7b ) and ( 2.21a )-( 2.21b )

From: A class of quasi-variable mesh methods based on off-step discretization for the solution of non-linear fourth order ordinary differential equations with Dirichlet and Neumann boundary conditions

N   Second order ( C  = 0.45) Third order ( C  = 1.1)
  MAE RMSE MAE RMSE
10 u 2.3524e−06 1.2294e−06 3.3425e−09 2.1271e−09
\(u' \) 1.6070e−05 6.8720e−06 1.5594e−08 1.0533e−08
v 1.2026e−05 8.0087e−06 1.9955e−08 1.2704e−08
\(v' \) 3.9650e−05 2.8558e−05 1.0046e−07 5.9011e−08
20 u 7.4405e−07 3.8633e−07 1.5475e−09 1.0102e−09
\(u'\) 4.0111e−06 1.9062e−06 4.8890e−09 3.5842e−09
v 3.0216e−06 1.9569e−06 3.8218e−09 2.4468e−09
\(v' \) 9.9398e−06 6.9784e−06 1.3573e−08 8.9719e−09
40 u 1.9760e−07 1.0079e−07 2.7490e−10 1.7786e−10
\(u'\) 1.0611e−06 4.8541e−07 8.6380e−10 6.1758e−10
v 7.5983e−07 4.8342e−07 5.2919e−10 3.3868e−10
\(v' \) 2.4813e−06 1.7237e−06 1.7523e−09 1.1953e−09
Order u 1.9128 1.9385 2.49 2.51
\(u'\) 1.9185 1.9734 2.50 2.54
v 1.9916 2.0172 2.85 2.85
\(v' \) 2.0021 2.0173 2.95 2.91