Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

Table 1

A determination of the accuracy of RK4 for the Genesio system (1.1).

𝑡	Δ=|RK40.01−RK40.001|			Δ=|RK40.001−RK40.0001|
	Δ𝑥	Δ𝑦	Δ𝑧	Δ𝑥	Δ𝑦	Δ𝑧
1	2.130𝐸−10	1.525𝐸−10	6.681𝐸−10	2.12𝐸−14	1.58𝐸−14	6.68𝐸−14
2	3.299𝐸−10	8.467𝐸−10	9.038𝐸−10	3.36𝐸−14	8.40𝐸−14	9.30𝐸−14
3	4.957𝐸−10	1.443𝐸−09	2.394𝐸−09	4.85𝐸−14	1.461𝐸−13	2.362𝐸−13
4	1.533𝐸−09	9.664𝐸−10	5.188𝐸−09	1.540𝐸−13	9.27𝐸−14	5.232𝐸−13
5	3.154𝐸−10	4.876𝐸−09	1.175𝐸−09	3.51𝐸−14	4.884𝐸−13	1.044𝐸−13
6	3.474𝐸−09	2.279𝐸−09	1.324𝐸−08	3.455𝐸−13	2.380𝐸−13	1.322𝐸−12
7	3.567𝐸−09	8.028𝐸−09	9.569𝐸−09	3.631𝐸−13	7.955𝐸−13	9.820𝐸−13
8	3.430𝐸−09	1.243𝐸−08	1.969𝐸−08	3.341𝐸−13	1.257𝐸−12	1.942𝐸−12
9	1.132𝐸−08	5.660𝐸−09	3.797𝐸−08	1.135𝐸−12	5.373𝐸−13	3.824𝐸−12
10	1.655𝐸−09	2.685𝐸−08	2.350𝐸−09	1.881𝐸−13	2.688𝐸−12	1.640𝐸−13
11	1.674𝐸−08	1.348𝐸−08	7.314𝐸−08	1.667𝐸−12	1.402𝐸−12	7.308𝐸−12
12	2.241𝐸−08	4.278𝐸−08	6.208𝐸−08	2.270𝐸−12	4.234𝐸−12	6.351𝐸−12
13	1.873𝐸−08	5.370𝐸−08	6.170𝐸−08	1.822𝐸−12	5.436𝐸−12	6.050𝐸−12
14	3.733𝐸−08	2.187𝐸−08	1.333𝐸−07	3.770𝐸−12	2.083𝐸−12	1.348𝐸−11
15	1.595𝐸−08	1.228𝐸−07	1.926𝐸−08	1.679𝐸−12	1.232𝐸−11	1.565𝐸−12
16	7.856𝐸−08	4.718𝐸−08	2.002𝐸−07	7.808𝐸−12	4.950𝐸−12	1.999𝐸−11
17	1.317𝐸−08	7.821𝐸−08	9.779𝐸−08	1.510𝐸−12	7.839𝐸−12	1.008𝐸−11
18	2.585𝐸−08	8.743𝐸−08	1.959𝐸−07	2.601𝐸−12	9.132𝐸−12	1.983𝐸−11
19	9.424𝐸−08	6.053𝐸−08	2.934𝐸−07	9.655𝐸−12	5.883𝐸−12	3.032𝐸−11
20	5.455𝐸−08	4.084𝐸−08	1.401𝐸−07	5.290𝐸−12	4.470𝐸−12	1.423𝐸−11