Skip to main content

Table 15 Problem 6 : 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 scheme ( C  = 0.5) Third order scheme ( C  = 0.6)
u \(\boldsymbol {u'} \) u \(\boldsymbol {u'} \)
MAE RMSE MAE RMSE MAE RMSE MAE RMSE
8 2.254e−03 8.560e−03 1.521e−03 5.047e−03 2.40e−04 1.67e−04 7.48e−04 4.76e−04
16 5.225e−04 1.969e−03 3.401e−04 1.164e−03 2.17e−05 1.45e−05 8.88e−05 4.60e−05
32 1.259e−04 4.542e−04 7.999e−05 2.754e−04 2.19e−06 1.43e−06 8.30e−06 4.76e−06
64 3.091e−05 1.112e−04 1.945e−05 6.718e−05 2.43e−07 1.57e−07 8.73e−07 5.29e−07
Order 2.0266 2.0301 2.0395 2.0356 3.17 3.19 3.25 3.17