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

Table 1

Comparison of the results of the frequency and amplitude by the proposed SLM approach with the exact results and the homotopy analysis method results of Chen and Liu [9] when 𝜀=1.

Chen and Liu [9]			SLM results
Order	𝜔	𝛼	Order	𝜔	𝛼
10	0.94295340115	2.00861561331	2	0.93782084070	2.01344273793
20	0.94295586899	2.00861988872	4	0.94295585006	2.00861985316
50	0.94295584744	2.00861986087	6	0.94295584744	2.00861986087
100	0.94295584744	2.00861986087	8	0.94295584744	2.00861986087
Exact	0.94295584744	2.00861986087	Exact	0.94295584744	2.00861986087