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Table 16 Problem 7 : MAEs and RMSEs using ( 2.7a )-( 2.7b ) and ( 2.21a )-( 2.21b ) with \(\pmb{C=1}\)

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 Fourth order
  MAE RMSE MAE RMSE
10 u 7.1411e−06 4.8598e−06 1.5183e−08 1.0322e−08
\(u' \) 2.4886e−05 1.6832e−05 4.8261e−08 3.5393e−08
v 3.3399e−06 2.2408e−06 2.0788e−08 1.4229e−08
\(v' \) 1.1264e−05 8.1372e−06 7.3344e−08 4.6608e−08
20 u 1.8060e−06 1.1822e−06 9.4738e−10 6.2681e−10
\(u'\) 6.4868e−06 4.1284e−06 3.0174e−09 2.1522e−09
v 8.5494e−07 5.5949e−07 1.2768e−09 8.4967e−10
\(v' \) 2.6592e−06 1.9574e−06 4.7506e−09 2.9017e−09
40 u 4.5147e−07 2.9169e−07 5.9265e−11 3.8611e−11
\(u'\) 1.6208e−06 1.0204e−06 1.8898e−10 1.3259e−10
v 2.1498e−07 1.3896e−07 8.0073e−11 5.2627e−11
\(v' \) 6.7508e−07 4.8234e−07 3.0237e−10 1.8155e−10
Order u 2.0046 2.0092 4.00 4.02
Order \(u' \) 2.0020 2.0087 4.00 4.02
Order v 2.0253 2.0288 4.00 4.01
Order \(v' \) 2.0268 2.0305 3.97 4.00