A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method

Table 3

Comparison of the SLM results and the HAM and Homotopy-Padé [8] approximate results for 𝛼 at different orders 𝑝 for 𝛼 for 𝜀=10 and 𝜀=25.

HAM results [8]			Homotopy-Padé [8]			SLM results
𝑝	𝜀=10	𝜀=25	[𝑝, 𝑝]	𝜀=10	𝜀=10	𝑝	𝜀=10	𝜀=25
5	0.99833	1.01046	[2, 2]	0.99914	1.01167	1	1.01834916	1.00009888
10	0.99588	1.00313	[4, 4]	0.99651	1.00113	2	1.00142002	0.99994805
15	0.99624	1.00117	[6, 6]	0.99644	1.00012	3	0.99684045	0.99994004
20	0.99644	1.00049	[8, 8]	0.99644	0.99996	4	0.99643870	0.99993998
25	0.99644	1.00017	[10, 10]	0.99644	0.99994	5	0.99643534	0.99993998
30	0.99644	1.00000	[12, 12]	0.99644	0.99994	6	0.99643534	0.99993998