Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 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	K = 1			K = 10
x	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
0.1	5.1e−07	2.1e−10	1.7e−09	2.2e−06	1.7e−09	1.2e−09
0.2	1.6e−06	6.4e−10	5.8e−09	7.2e−06	5.2e−09	4.3e−09
0.3	2.9e−06	1.1e−09	1.1e−08	1.3e−05	9.0e−09	8.2e−09
0.4	3.9e−06	1.5e−09	1.6e−08	1.7e−05	1.2e−08	1.2e−08
0.5	4.4e−06	1.7e−09	2.1e−08	2.0e−05	1.3e−08	1.5e−08
0.6	4.2e−06	1.6e−09	2.2e−08	1.9e−05	1.3e−08	1.6e−08
0.7	3.3e−06	1.3e−09	2.0e−08	1.6e−05	1.0e−08	1.5e−08
0.8	2.0e−06	7.5e−10	1.4e−08	9.5e−06	6.2e−09	1.1e−08
0.9	6.2e−07	2.3e−10	5.6e−08	3.2e−06	1.9e−09	4.5e−09
1.0	0.0e+00	0.0e+00	0.0e+00	0.0e+00	0.0e+00	0.0e+00

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