A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence

Table 3

Comparison of the results for solution of Painlevé I.

T	𝑦𝑀 (𝑡)	Results for 𝑢(𝑡)		Proposed Results 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