A Numerical Convolution Representation of Potential for a Disk Surface Density in 3D

Table 2

The errors and order accuracy of the proposed method on polar coordinates for various number of zones, 𝑁=2^𝑘 from 𝑘=5 to 9 for the 𝐷₂ disk. This table shows that the accuracy is only first order.

𝑁𝑘	𝐸^1	𝐸^2	𝐸^∞	𝑁𝑘−1/𝑁𝑘	𝑂^1	𝑂^2	𝑂^∞
32	4.43𝐸−2	3.62𝐸−2	5.25𝐸−2
64	1.38𝐸−2	1.47𝐸−2	2.33𝐸−2	32/64	1.68	1.30	1.17
128	5.89𝐸−3	7.00𝐸−3	1.13𝐸−2	64/128	1.23	1.07	1.04
256	2.77𝐸−3	3.42𝐸−3	5.58𝐸−3	128/256	1.08	1.03	1.02
512	1.48𝐸−3	1.68𝐸−4	2.76𝐸−3	256/512	0.90	1.03	1.02