Higher-Order Solutions of Coupled Systems Using the Parameter Expansion Method

Table 1

Comparison of approximate and exact periods for Case  1.

Constant parameters						Approximate solutions		Exact solution	|𝑇−𝑇ex|/𝑇ex
𝑚	𝑙	𝑝	𝑘1	𝑘3	𝐴	𝑇1	𝑇2	𝑇𝑒	𝑇=𝑇1	𝑇=𝑇2
1	1	1	10	5	1	1.96254	1.96451	1.96451	0.101%	0.000%
5	1.5	5	5	6	3	3.23743	3.32518	3.32368	2.664%	0.045%
10	10	10	10	50	10	0.32418	0.33145	0.33143	2.210%	0.031%
50	25	40	30	100	20	0.25640	0.26216	0.26208	2.216%	0.031%
70	20	−30	50	100	10	0.60486	0.61827	0.61809	2.187%	0.030%
100	50	150	70	20	100	0.16221	0.16586	0.16580	2.218%	0.031%
500	150	220	120	500	0.5	9.67637	9.71682	9.71672	0.417%	0.001%
1000	500	1000	500	500	1	6.73241	6.75877	6.75871	0.391%	0.001%