A new numerical approach to solve Thomas–Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming

Raja, Muhammad Asif Zahoor; Zameer, Aneela; Khan, Aziz Ullah; Wazwaz, Abdul Majid

doi:10.1186/s40064-016-3093-5

SpringerPlus

Table 2 Results of statistical indices for each case of all five scenarios of Thomas–Fermi equation

From: A new numerical approach to solve Thomas–Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming

Scenario	t	Case 1			t	Case 2			t	Case 3
Scenario	t	Min	Mean	SD	t	Min	Mean	SD	t	Min	Mean	SD
1	0.1	0.851971	0.851971	4.52E−12	0.05	0.920142	0.920142	6.08E−12	0.02	0.96585	0.96585	3.51E−11
	0.3	0.62099	0.62099	8.72E−12	0.25	0.672508	0.672508	2.36E−11	0.26	0.661314	0.661314	1.27E−10
	0.5	0.428691	0.428691	9.18E−12	0.45	0.473805	0.473805	3.37E−11	0.5	0.427647	0.427647	4.20E−10
	0.7	0.253065	0.253065	6.81E−12	0.65	0.295554	0.295554	3.19E−11	0.74	0.21841	0.21841	4.27E−10
	0.9	0.083907	0.083907	2.47E−12	0.85	0.125711	0.125711	1.72E−11	0.98	0.016734	0.016734	4.78E−11
2	0.5	0.626064	0.626064	4.02E−11	0.25	0.763272	0.763272	8.48E−11	0.1	0.883944	0.883944	1.37E−10
	1.5	0.315987	0.315987	1.15E−10	1.25	0.36109	0.36109	4.17E−10	1.3	0.34772	0.34772	1.80E−09
	2.5	0.17976	0.17976	1.67E−10	2.25	0.20325	0.20325	6.86E−10	2.5	0.175894	0.175894	3.02E−09
	3.5	0.096649	0.096649	1.61E−10	3.25	0.113205	0.113205	7.48E−10	3.7	0.081102	0.081102	2.77E−09
	4.5	0.031067	0.031067	7.40E−11	4.25	0.046107	0.046107	4.65E−10	4.9	0.006074	0.006074	3.14E−10
3	2.5	0.264695	0.264695	2.36E−09	1	0.465685	0.465685	9.48E−10	0.5	0.627672	0.627672	3.37E−10
	7.5	0.048052	0.048052	2.12E−08	6	0.062298	0.062298	1.82E−08	6.5	0.052959	0.052959	1.65E−08
	12.5	0.017323	0.017323	5.87E−08	11	0.020782	0.020782	6.17E−08	12.5	0.015596	0.015596	5.91E−08
	17.5	0.007506	0.007507	8.53E−08	16	0.00898	0.00898	1.07E−07	18.5	0.005748	0.005748	8.54E−08
	22.5	0.002241	0.002241	5.16E−08	21	0.003412	0.003412	9.43E−08	24.5	0.000409	0.000409	1.33E−08
4	5	0.154691	0.154691	7.11E−09	2	0.308917	0.308917	4.73E−08	0.5	0.627672	0.627672	3.08E−10
	15	0.013087	0.013087	1.56E−07	12	0.018663	0.018664	2.66E−06	12.5	0.053001	0.053001	2.05E−08
	25	0.003821	0.003821	5.80E−07	22	0.004943	0.004949	1.26E−05	24.5	0.015904	0.015904	1.07E−07
	35	0.001523	0.001524	9.78E−07	32	0.001918	0.001931	2.60E−05	36.5	0.006928	0.006929	2.94E−07
	45	0.000442	0.000442	6.49E−07	42	0.000699	0.000711	2.52E−05	48.5	0.003631	0.003631	5.66E−07
5	5	0.154691	0.154691	2.88E−07	2	0.308917	0.308917	4.60E−08	1	0.465686	0.465686	1.44E−08
	25	0.003863	0.003908	2.92E−05	26	0.003357	0.003378	2.47E−05	25	0.003554	0.003557	1.67E−05
	45	0.000886	0.001081	0.00011	50	0.000663	0.000766	0.000107	49	0.000679	0.000695	7.55E−05
	65	0.000326	0.000663	0.000169	74	0.000228	0.000385	0.000152	73	0.000229	0.000253	0.000109
	85	0.000117	0.000409	0.000141	98	1.85E−05	4.59E−05	2.65E−05	97	2.55E−05	3.08E−05	2.42E−05

Back to article page