Boundary Value Problems

Table 5 IVP ( 49 ): Convergence of the collocation scheme, $k = 4$

From: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity

h	Equidistant points			Gaussian points
	Uniform			Mesh			Uniform
	${∥ Y_{h} - Y ∥}_{\infty}$	c	p	${∥ Y_{h} - Y ∥}_{\infty}$	c	p	${∥ Y_{h} - Y ∥}_{\infty}$	c	p
1/2	3.2e–03	–	–	6.2e–04	–	–	1.2e–03	–	–
1/4	1.1e–03	1.0e–01	1.49	2.2e–04	1.7e–03	1.50	4.4e–04	1.9e–01	1.50
1/8	4.1e–04	1.0e–01	1.50	7.7e–05	1.7e–03	1.50	1.6e–04	1.9e–01	1.50
1/16	1.4e–04	1.0e–01	1.50	2.7e–05	1.7e–03	1.50	5.5e–05	1.9e–01	1.50
1/32	5.1e–05	1.0e–01	1.50	9.6e–06	1.7e–03	1.50	1.9e–05	1.9e–01	1.50
1/64	1.8e–05	1.0e–01	1.50	3.4e–06	1.7e–03	1.50	2.4e–04	3.6e–15	−3.65
1/128	8.0e–05	7.4e–11	−2.15	1.2e–06	1.7e–03	1.50	4.9e–03	3.4e–17	−4.34
1/356	7.9e–04	4.0e–14	−3.31	4.3e–07	1.7e–03	1.50	1.0e–01	2.1e–17	−4.40
1/512	2.5e–02	2.5e–19	−4.99	1.5e–07	1.7e–03	1.50	4.8e–01	1.5e–09	−2.20

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