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Table 13 Problem 5 : MAEs and RMSEs using ( 2.21a )-( 2.21b ) with different values of C

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

λ N   Uniform mesh ( C  = 1) Quasi-variable mesh ( C  = 0.7)
MAE RMSE MAE RMSE
1 16 u 1.59e−07 1.20e−08 1.01e−06 4.22e−08
\(u' \) 5.68e−07 3.72e−07 3.29e−06 1.59e−06
32 u 1.00e−08 2.13e−10 1.11e−07 1.20e−09
\(u' \) 3.55e−08 1.34e−08 3.52e−07 9.15e−08
64 u 6.29e−10 3.54e−12 1.29e−08 3.57e−11
order 4.00 5.91 3.10 5.07
\(u' \) 2.23e−09 4.49e−10 4.10e−08 5.47e−09
order 4.00 4.90 3.10 4.06
10 16 u 9.90e−07 1.24e−07 2.08e−06 1.58e−07
\(u' \) 4.63e−06 3.69e−06 8.43e−06 5.61e−06
32 u 6.20e−08 2.25e−09 1.82e−07 3.64e−09
\(u' \) 2.85e−07 1.40e−07 7.32e−07 2.70e−07
64 u 3.88e−09 3.79e−11 1.82e−08 9.09e−11
order 4.00 5.89 3.33 5.32
\(u' \) 1.77e−08 4.78e−09 7.18e−08 1.38e−08
order 4.01 4.87 3.35 4.30
100 16 u 5.57e−06 1.55e−06 7.17e−06 1.33e−06
\(u' \) 3.70e−05 3.70e−05 3.99e−05 3.99e−05
32 u 3.30e−07 3.14e−08 4.53e−07 2.65e−08
\(u' \) 2.18e−06 1.77e−06 2.55e−06 1.82e−06
64 u 2.03e−08 5.59e−10 3.36e−08 5.33e−10
order 4.02 5.81 3.75 5.64
\(u' \) 1.34e−07 6.76e−08 1.89e−07 7.79e−08
order 4.02 4.71 3.75 4.55