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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Problem 2 : MAEs using ( 2.7a )-( 2.7b ) and ( 2.21a )-( 2.21b ) with \(\pmb{C=1}\)

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