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Table 2 Problem 1 : Absolute errors 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

x \(\boldsymbol {K=10^{2}}\) \(\boldsymbol {K=10^{3}} \) \(\boldsymbol {K=10^{6}} \)
Second order ( 2.7a )-( 2.7b ) Fourth order ( 2.21a )-( 2.21b ) Absolute error [ 17 ] Second order ( 2.7a )-( 2.7b ) Fourth order ( 2.21a )-( 2.21b ) Absolute error [ 17 ] Second order ( 2.7a )-( 2.7b ) Fourth order ( 2.21a )-( 2.21b ) Absolute error [ 17 ]
0.0 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00
0.1 9.2e−06 7.9e−09 1.2e−11 2.4e−05 1.8e−08 1.5e−14 6.9e−04 2.1e−08 1.5e−10
0.2 2.7e−05 2.0e−08 4.0e−11 4.9e−05 3.4e−08 2.9e−13 3.8e−05 3.6e−08 3.7e−08
0.3 4.4e−05 3.3e−08 8.5e−11 7.0e−05 4.8e−08 3.1e−12 7.2e−04 4.8e−08 9.0e−07
0.4 5.8e−05 4.2e−08 1.6e−10 8.7e−05 5.8e−08 1.9e−11 7.0e−05 2.1e−10 8.5e−06
0.5 6.6e−05 4.7e−08 2.9e−10 9.8e−05 6.4e−08 7.4e−11 7.5e−04 5.7e−08 4.8e−05
0.6 6.7e−05 4.6e−08 5.1e−10 1.0e−04 6.4e−08 2.0e−10 8.5e−05 6.3e−08 1.9e−04
0.7 5.8e−05 3.9e−08 7.4e−10 9.5e−05 5.7e−08 3.9e−10 7.7e−04 5.7e−08 6.4e−04
0.8 4.0e−05 2.5e−08 8.1e−10 7.8e−05 4.1e−08 5.1e−10 6.7e−05 4.3e−08 1.7e−03
0.9 1.5e−05 8.5e−09 4.7e−10 4.5e−05 1.5e−08 3.4e−10 7.7e−04 2.0e−08 4.2e−03
1.0 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00