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Table 12 Problem 5 : MAEs and RMSEs using ( 2.7a )-( 2.7b ) 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  = 0.6)
MAE RMSE MAE RMSE
1 8 u 1.79e−04 1.13e−04 4.34e−05 2.60e−05
\(u' \) 6.45e−04 4.21e−04 1.35e−04 8.96e−05
16 u 4.65e−05 2.95e−05 9.98e−06 5.92e−06
\(u' \) 1.52e−04 1.04e−04 3.33e−05 2.18e−05
32 u 1.17e−05 7.46e−06 2.44e−06 1.45e−06
\(u' \) 3.75e−05 2.60e−05 8.57e−06 5.41e−06
64 u 2.94e−06 1.87e−06 6.07e−07 3.59e−07
\(u' \) 9.35e−06 6.51e−06 2.15e−06 1.35e−06
128 u 7.36e−07 4.68e−07 1.52e−07 8.97e−08
\(u' \) 2.33e−06 1.63e−06 5.40e−07 3.38e−07
256 u 1.84e−07 1.17e−07 2.69e−08 1.51e−08
order 2.00 2.00 2.49 2.57
\(u' \) 5.83e−07 4.06e−07 1.04e−07 6.32e−08
order 2.00 2.00 2.38 2.42
10 8 u 1.40e−03 8.98e−04 1.29e−03 8.40e−04
\(u' \) 4.36e−03 3.12e−03 4.05e−03 2.91e−03
16 u 3.47e−04 2.22e−04 3.26e−04 2.06e−04
\(u' \) 1.11e−03 7.68e−04 1.00e−03 7.18e−04
32 u 8.64e−05 5.53e−05 8.11e−05 5.14e−05
\(u' \) 2.75e−04 1.91e−04 2.51e−04 1.79e−04
64 u 2.16e−05 1.38e−05 2.03e−05 1.28e−05
\(u' \) 6.89e−05 4.78e−05 6.29e−05 4.47e−05
128 u 5.40e−06 3.46e−06 5.06e−06 3.21e−06
\(u' \) 1.72e−05 1.19e−05 1.57e−05 1.12e−05
256 u 1.35e−06 8.64e−07 1.26e−06 7.95e−07
order 2.00 2.00 2.01 2.01
\(u' \) 4.30e−06 2.99e−06 3.90e−06 2.77e−06
order 2.00 2.00 2.01 2.01
100 8 u 4.03e−03 2.70e−03 4.04e−03 2.72e−03
\(u' \) 1.34e−02 8.99e−03 1.41e−02 9.05e−03
16 u 9.68e−04 6.46e−04 9.80e−04 6.46e−04
\(u' \) 3.21e−03 2.16e−03 3.20e−03 2.18e−03
32 u 2.40e−04 1.60e−04 2.42e−04 1.60e−04
\(u' \) 8.06e−04 5.35e−04 7.87e−04 5.38e−04
64 u 5.99e−05 3.98e−05 6.04e−05 3.98e−05
\(u' \) 2.01e−04 1.33e−04 1.96e−04 1.34e−04
128 u 1.50e−05 9.95e−06 1.51e−05 9.93e−06
\(u' \) 5.02e−05 3.33e−05 4.89e−05 3.35e−05
256 u 3.74e−06 2.49e−06 3.77e−06 2.48e−06
order 2.00 2.00 2.00 2.00
\(u' \) 1.25e−05 8.33e−06 1.22e−05 8.37e−06
order 2.00 2.00 2.00 2.00