Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 14 Problem 6 : MAEs and RMSEs 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 method				Fourth order method
	u		\(\boldsymbol {u'} \)		u		\(\boldsymbol {u'} \)
	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
8	9.512e−04	6.737e−04	3.162e−03	2.137e−03	5.80e−05	3.97e−05	1.55e−04	9.83e−05
16	2.212e−04	7.021e−04	1.501e−04	4.995e−04	3.68e−06	2.44e−06	1.94e−05	7.78e−06
32	5.410e−05	1.729e−04	3.576e−05	1.206e−04	2.36e−07	1.54e−07	1.67e−06	5.65e−07
64	1.339e−05	4.298e−05	8.769e−06	2.972e−05	1.51e−08	9.75e−09	1.23e−07	3.86e−08
128	3.337e−06	1.073e−05	2.175e−06	7.386e−06	9.64e−10	6.19e−10	8.43e−09	2.54e−09
256	8.335e−07	2.682e−06	5.421e−07	1.841e−06	3.66e−11	2.45e−11	5.37e−10	1.68e−10
Order	2.0015	2.0001	2.0046	2.0038	4.72	4.66	3.97	3.92

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