Table 3.

Comparison of the results for solution of Painlevé I.

T	y M(t)	Results for u(t)		Proposed Results $\widehat{y}(t)$
		VIM	HPM	PSO	PSO-ASA
0.1	0.1002167469	0.1002167477	0.1002167477	0.101267314	0.100211733
0.2	0.2021394539	0.2021394527	0.2021394527	0.202944631	0.202137722
0.3	0.3086307548	0.3086307489	0.3086307492	0.309301843	0.308629917
0.4	0.4239862999	0.4239862788	0.4239862895	0.424625376	0.423985302
0.5	0.5543401416	0.5543399112	0.5543401182	0.555018673	0.554341815
0.6	0.7084621313	0.7084596600	0.7084620603	0.709234588	0.708467300
0.7	0.8992500131	0.8992296942	0.8992493803	0.900159983	0.899254787
0.8	1.1465318491	1.1463982509	1.1465240263	1.147598102	1.146541253
0.9	1.4825246345	1.4817789520	1.4824439956	1.483815424	1.482531252
1.0	1.9631285609	1.9594210423	1.9624483064	1.965104083	1.963204324