Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

Table 1

Numerical comparison of Thomas-Fermi’s numerical solution [39] and approximations [15, 38] and (45).

	Numerical [39]	[38]	(45)	[15]
0.00	—	1.000000000	1.000000000	1.000000000
0.25	0.755880759	0.776191000	0.708502932	0.680650028
0.50	0.606700008	0.615917000	0.570491745	0.459455663
0.75	0.502964042	0.505380000	0.485018011	0.307042537
1.00	0.424333179	0.423772000	0.421167227	0.202655526
1.25	0.363227937	0.362935000	0.369542163	0.131667603
1.50	0.314660642	0.314490000	0.326298526	0.083800106
1.75	0.275233848	0.275154000	0.289315779	0.051853222
2.00	0.242678587	0.242718000	0.257253699	0.030801947
2.25	0.215439334	0.215630000	0.229210094	0.017153465
2.50	0.192406328	0.192795000	0.204540381	0.008491277
2.75	0.172758691	0.173364000	0.182755264	0.003152503
3.00	0.155871862	0.156719000	0.163464474	0
3.25	0.141260504	0.142371000	0.146346052
3.50	0.128541381	0.129937000	0.131128799
3.75	0.117408054	0.119108000	0.117581337
4.00	0.107612958	0.109632000	0.105504623
4.25	0.098954329	0.101303000	0.094726427
4.50	0.091266456	0.093950400	0.085097045
4.75	0.084412289	0.087432000	0.076485875
5.00	0.078277758	0.081629600	0.068778618