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Table 4 Problem 3 : MAEs using ( 2.7a )-( 2.7b ) 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

λ 1 10 \(\boldsymbol {10^{2}} \) \(\boldsymbol {10^{3}} \) \(\boldsymbol {10^{4}} \)
N u \(\boldsymbol {u'} \) u \(\boldsymbol {u'} \) u \(\boldsymbol {u'} \) u \(\boldsymbol {u'} \) u \(\boldsymbol {u'} \)
8 7.11e−07 2.36e−05 1.61e−04 1.21e−03 5.25e−03 3.95e−02 3.48e−02 2.57e−01 1.29e−01 7.07e−01
16 4.61e−07 3.84e−06 4.46e−05 3.03e−04 1.31e−03 9.53e−03 7.96e−03 1.19e−01 3.89e−02 4.31e−01
32 1.36e−07 8.95e−07 1.15e−05 7.85e−05 3.27e−04 2.27e−03 1.94e−03 3.21e−02 7.36e−03 2.48e−01
64 3.51e−08 2.42e−07 2.90e−06 1.98e−05 8.21e−05 5.69e−04 4.84e−04 7.28e−03 1.83e−03 8.49e−02
128 8.86e−09 6.16e−08 7.27e−07 4.96e−06 2.05e−05 1.42e−04 1.21e−04 1.78e−03 4.58e−04 1.94e−02
256 2.29e−09 1.50e−08 1.82e−07 1.24e−06 5.13e−06 3.55e−05 3.03e−05 4.43e−04 1.14e−04 4.60e−03
Order 1.95 2.04 2.00 2.00 2.00 2.00 2.00 2.01 2.00 2.08