Generalized Abel Inversion Using Extended Hat Functions Operational Matrix

Table 3

The absolute errors 𝐸_𝑘(𝑟), at different nodal points 𝑟, for 𝑛=3000,2000, and 1000.

	𝑛	𝑟=0.0	𝑟=0.2	𝑟=0.4	𝑟=0.6	𝑟=0.8	𝑟=1.0
𝐸0(𝑟)	3000	0	1.9712×10^−9	1.5849×10^−8	5.361×10^−8	1.2724×10^−7	2.4875×10^−7
	2000	0	4.4178×10^−7	3.5563×10^−8	1.2035×10^−7	2.8575×10^−7	5.5872×10^−7
	1000	0	1.7515×10^−8	1.4137×10^−7	4.7899×10^−7	1.138×10^−6	2.2262×10^−6
𝐸1(𝑟)	3000	4.6073×10^−6	1.5029×10^−6	2.5454×10^−6	5.3295×10^−7	7.3491×10^−7	2.0451×10^−6
	2000	1.0031×10^−5	1.1159×10^−6	4.5957×10^−6	2.3615×10^−7	4.4563×10^−6	9.2247×10^−7
	1000	1.7061×10^−5	7.7631×10^−6	7.528×10^−6	4.4903×10^−6	1.5261×10^−5	4.2806×10^−6
𝐸2(𝑟)	3000	0.0061012	0.0011742	0.0011595	0.0039968	0.00064593	0.0029774
	2000	0.0068177	0.0068177	0.00078732	0.00067568	0.0016351	4.2642×10^−5
	1000	0.0001341	0.00067286	0.0010734	0.00040813	0.00098541	0.00074723