Boundary Value Problems

Table 4 IVP ( 47 ), ( 48 ): 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	2.7e–05	–	–	6.9e–07	–	–	2.6e–05	–	–
1/4	9.1e–07	2.2e+00	4.91	5.8e–09	8.2e–05	6.90	8.6e–07	3.7e+02	4.90
1/8	2.9e–08	2.7e+00	4.98	4.7e–11	8.7e–05	6.95	2.7e–08	5.0e+02	4.98
1/16	9.0e–10	2.9e+00	5.00	3.7e–13	9.3e–05	6.97	8.6e–10	5.4e+02	5.00
1/32	2.8e–11	2.9e+00	5.00	6.2e–15	4.7e–06	5.90	2.7e–11	5.6e+02	5.00
1/64	8.8e–13	3.1e+00	5.01	1.5e–14	7.4e–17	−1.28	8.4e–13	5.8e+02	5.01
1/128	3.1e–14	1.2e+00	4.84	8.9e–15	3.6e–13	0.77	2.4e–14	1.1e+03	5.10
1/256	2.7e–15	2.4e–04	3.52	7.1e–15	4.2e–14	0.32	3.1e–15	1.3e–04	2.97
1/512	1.3e–15	3.4e–12	1.00	1.3e–14	4.7e–17	−0.91	3.6e–15	6.4e–16	−0.19

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