An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry

Table 1

Approximate solutions for 𝑁=24.

𝑟	𝛼=𝛽=−1/2	𝛼=𝛽=0	𝛼=𝛽=1/2	𝛼=𝛽=−1/2	𝛼=𝛽=0	𝛼=𝛽=1/2
	(𝑛=5,𝜆=1/2)			(𝑛=3,𝜆=4/3)
0.0	0.847890	0.847890	0.847890	1.26779	1.26779	1.26779
0.1	0.849462	0.849462	0.849462	1.26418	1.26418	1.26418
0.2	0.854173	0.854173	0.854173	1.125350	1.125350	1.125350
0.3	0.862013	0.862013	0.862013	1.23616	1.23616	1.23616
0.4	0.872959	0.872959	0.872959	1.21283	1.21283	1.21283
0.5	0.886976	0.886976	0.886976	1.18437	1.18437	1.18437
0.6	0.904009	0.904009	0.904009	1.15174	1.15174	1.15174
0.7	0.923974	0.923974	0.923974	1.11599	1.11599	1.11599
0.8	0.946751	0.946751	0.946751	1.07815	1.07815	1.07815
0.9	0.972170	0.972170	0.972170	1.03918	1.03918	1.03918
1.0	1.000000	1.000000	1.000000	1.00000	1.00000	1.00000