Generalized Abel Inversion Using Extended Hat Functions Operational Matrix

Table 5

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	5.4281×10^−7	2.8998×10^−7	1.5818×10^−7	2.6121×10^−8	1.0578×10^−7	2.9684×10^−7
	2000	1.2088×10^−6	6.5113×10^−7	3.5535×10^−7	5.887×10^−8	2.3717×10^−7	6.5839×10^−7
	1000	4.7364×10^−6	2.5925×10^−6	1.4164𝑒×10^−6	2.3637×10^−7	9.4123×10^−7	2.559×10^−6
𝐸1(𝑟)	3000	6.8261×10^−6	2.1337×10^−6	2.2043×10^−6	1.4765×10^−6	1.4642×10^−6	3.421×10^−6
	2000	1.589×10^−6	5.7191×10^−6	2.8577×10^−6	2.5629×10^−6	4.4183×10^−6	3.9074×10^−8
	1000	1.9156×10^−5	4.4716×10^−6	1.643×10^−5	1.712×10^−5	3.6022×10^−6	3.6477×10^−6
𝐸2(𝑟)	3000	0.01495	0.020628	0.021094	0.065933	0.011844	0.095356
	2000	0.022427	0.010769	0.024946	0.014392	0.0068535	0.028831
	1000	0.056845	0.033342	0.013319	0.018905	0.028086	0.045314