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Table 14 Problem 6 : 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 method Fourth order method
u \(\boldsymbol {u'} \) u \(\boldsymbol {u'} \)
MAE RMSE MAE RMSE MAE RMSE MAE RMSE
8 9.512e−04 6.737e−04 3.162e−03 2.137e−03 5.80e−05 3.97e−05 1.55e−04 9.83e−05
16 2.212e−04 7.021e−04 1.501e−04 4.995e−04 3.68e−06 2.44e−06 1.94e−05 7.78e−06
32 5.410e−05 1.729e−04 3.576e−05 1.206e−04 2.36e−07 1.54e−07 1.67e−06 5.65e−07
64 1.339e−05 4.298e−05 8.769e−06 2.972e−05 1.51e−08 9.75e−09 1.23e−07 3.86e−08
128 3.337e−06 1.073e−05 2.175e−06 7.386e−06 9.64e−10 6.19e−10 8.43e−09 2.54e−09
256 8.335e−07 2.682e−06 5.421e−07 1.841e−06 3.66e−11 2.45e−11 5.37e−10 1.68e−10
Order 2.0015 2.0001 2.0046 2.0038 4.72 4.66 3.97 3.92