A Note on Fourth Order Method for Doubly Singular Boundary Value Problems

Table 1

Maximum absolute errors and order of the methods for Example 4.1.

𝑁	𝑏0=0.1	Order	𝑏0=0.5	Order	𝑏0=0.1	Order	𝑏0=0.5	Order
	𝑦(0)=ln(1/4)and𝜃=0.01				𝑦(0)=ln(1/4)and𝜃=0.98
32	8.23 (−7)^a		1.10 (−6)		6.11 (−7)		8.11 (−7)
64	5.05 (−8)	4.03	6.80 (−8)	4.02	3.50 (−8)	4.13	4.60 (−8)	4.14
128	3.13 (−9)		4.22 (−9)		2.09 (−9)		2.72 (−9)
256	1.94 (−10)	4.01	2.64 (−10)	4.00	1.27 (−10)	4.04	1.67 (−10)	4.03
	𝑦^′(0)=0and𝜃=0.01				𝑦^′(0)=0and𝜃=0.98
32	3.37 (−7)		4.03 (−7)		1.72 (−7)		1.95 (−7)
64	2.04 (−8)	4.05	2.46 (−8)	4.03	9.13 (−9)	4.24	9.80 (−9)	4.31
128	1.25 (−9)		1.52 (−9)		5.20 (−10)		5.39 (−10)
266	7.74 (−11)	4.02	9.56 (−11)	3.99	3.09 (−11)	4.08	3.23 (−11)	4.06

^a8.23(−7)=8.23×10⁻⁷.