Approximate Periodic Solution for the Nonlinear Helmholtz-Duffing Oscillator via Analytical Approaches

Table 2

Comparison between MMA, FHA, SHA, FGEM, and SGEM results with exact ones and HPM responses ().

		(relative error %)	(relative error %)	(relative error %)	(relative error %)	[39]; (relative error %)
0.01	6.283133	6.26977721; (0.2125657)	6.28305278; (0.0012767)	6.2698934; (0.2107154)	6.28305278; (0.0012767)	6.283132; (0.0000159)
0.05	6.281851	6.21470929; (1.0688203)	6.27987482; (0.0314585)	6.21530801; (1.0592895)	6.27987515; (0.0314630)	6.281831; (0.0003184)
0.1	6.277721	6.14291226; (2.1474152)	6.26997826; (0.1233367)	6.14414741; (2.1277402)	6.26998356; (0.1234043)	6.277642; (0.0012584)
10	1.004172	0.9610403; (4.2952461)	0.99830911; (0.5838523)	0.96753201; (3.6487768)	1.02917191; (2.4291285)	0.98321194; (2.087298)
20	0.5143428	0.4975256; (3.2696323)	0.50439032; (1.9349883)	0.50101412; (2.5914005)	0.52050519; (1.1839256)	0.50328477; (2.14993)
50	0.2082766	0.2028184; (2.6206285)	0.20235575; (2.8427777)	0.20426634; (1.9254484)	0.20888151; (0.2895968)	0.20375994; (2.168587)
100	0.1045213	0.1020148; (2.3980756)	0.10122095; (3.1575832)	0.10274684; (1.6976947)	0.10448959; (0.0303460)	0.1022518; (2.171328)