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Table 5 Problem 3 : MAEs using ( 2.7a )-( 2.7b ) with \(\pmb{C=\sqrt{\lambda}}\) for \(\pmb{0< x<\frac{1}{2}}\) and \(\pmb{C=\frac {1}{\sqrt{\lambda}}}\) for \(\pmb{\frac{1}{2} \leq x <1}\)

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 \(\boldsymbol {10^{2}} \) \(\boldsymbol {10^{4}} \) \(\boldsymbol {10^{6}} \) \(\boldsymbol {10^{8}} \)
N u \(\boldsymbol {u'}\) u \(\boldsymbol {u'}\) u \(\boldsymbol {u'}\) u \(\boldsymbol {u'}\)
32 2.50e−04 2.15e−03 9.24e−04 2.71e−02 1.74e−02 1.36e−01 1.97e−01 1.48e+00
64 6.12e−05 5.72e−04 2.84e−04 7.84e−03 2.43e−04 1.74e−02 7.29e−02 7.06e−01
128 1.50e−05 1.45e−04 7.31e−05 1.96e−03 1.85e−05 4.65e−03 3.26e−06 8.23e−03
256 3.74e−06 3.64e−05 1.84e−05 4.91e−04 4.72e−06 1.16e−03 8.49e−07 2.07e−03
Order 2.01 1.99 1.99 2.00 1.97 2.00 1.94 1.99