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Table 3 Problem 2 : MAEs 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 Fourth order Method given by [ 20 ] Method given by [ 21 ]
ϵ = 1/16
16 5.7082e−07 4.94e−09 1.7094e−04 1.666e−06
32 4.0505e−08 7.72e−11 4.7425e−05 1.31e−07
64 2.6061e−09 1.06e−12 1.2094e−05 2.614e−09
128 1.6406e−10 1.20e−14 3.0303e−06 6.716e−11
Order 3.9896 6.47   
ϵ = 1/32
16 2.9413e−07 2.51e−09 4.4022e−5 8.537e−07
32 2.0827e−08 3.78e−11 1.2203e−5 6.736e−08
64 1.3400e−09 4.66e−13 3.1220e−06 1.344e−09
128 8.4357e−11 5.10e−15 7.7974e−07 3.452e−11
Order 3.9896 6.51   
ϵ = 1/64
16 1.5656e−07 1.29e−09 1.1706e−05 4.520e−07
32 1.1037e−08 1.81e−11 3.2459e−06 3.569e−08
64 7.1086e−10 1.99e−13 8.2662e−07 7.128e−10
128 4.4747e−11 2.0714e−07 1.829e−11
Order 3.9897 6.51   
ϵ = 1/128
16 9.0137e−08 7.06e−10 2.60e−07
32 6.3500e−09 9.09e−12 2.049e−08
64 4.0842e−10 8.19e−14 4.092e−10
128 2.5709e−11 1.05e−11
Order 3.9897 6.79