Spectral Fixed Point Method for Nonlinear Oscillation Equation with Periodic Solution

Table 3

The 𝛽_opt, Res_𝑛, and CPU time (seconds).

Order; 𝑛	SFPM-SDS (𝑁SDS=5; 𝛿=10^−16)			SFPM-SDS (𝑁SDS=10; 𝛿=10^−16)
	𝛽𝑛,opt	Res𝑛	CPU (s)	𝛽𝑛,opt	Res𝑛	CPU (s)
1	0.6195087	0.011092067	0.31	0.6195087	0.011092067	0.31
2	0.6696290	6.005123𝑒−4	0.32	0.6696290	6.005123𝑒−4	0.32
3	0.6319373	5.224107𝑒−5	0.56	0.6319373	5.224107𝑒−5	0.56
4	0.6797179	4.408895𝑒−6	1.7	0.6797179	4.408895𝑒−6	1.7
5	0.6317019	4.341748𝑒−7	2.6	0.6317019	4.341748𝑒−7	2.6
6	(0.6317019)	4.324532𝑒−8	0.14	0.6874748	4.067318𝑒−8	3.0
7	(0.6317019)	4.872231𝑒−9	0.15	0.6299683	4.158791𝑒−9	3.3
8	(0.6317019)	5.515471𝑒−10	0.15	0.6928416	4.080293𝑒−10	3.7
9	(0.6317019)	6.640356𝑒−11	0.15	0.6281442	4.247500𝑒−11	4.0
10	(0.6317019)	8.019986𝑒−12	0.15	0.6969528	4.271866𝑒−12	4.1
11	(0.6317019)	9.979502𝑒−13	0.15	(0.6969528)	4.963906𝑒−13	0.15
12	(0.6317019)	1.244679𝑒−13	0.15	(0.6969528)	6.181212𝑒−14	0.15
13	(0.6317019)	1.576183𝑒−14	0.15	(0.6969528)	8.641084𝑒−15	0.15
14	(0.6317019)	2.000453𝑒−15	0.15	(0.6969528)	1.252247𝑒−15	0.15
15	(0.6317019)	2.560610𝑒−16	0.16	(0.6969528)	1.918912𝑒−16	0.15