Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

Table 2

Differences between 10-term HPM and 10-term MHPM with RK4 solutions on Δ𝑡=0.001.

𝑡	Δ=|HPM−RK40.001|			Δ=|MHPM0.001−RK40.001|
	Δ𝑥	Δ𝑦	Δ𝑧	Δ𝑥	Δ𝑦	Δ𝑧
1	1.856𝐸−05	6.289𝐸−05	0.0002355	2.12𝐸−14	1.58𝐸−14	6.68𝐸−14
2	0.01626	0.04539	0.2211	3.36𝐸−14	8.40𝐸−14	9.30𝐸−14
3	0.8815	1.912	10.73	4.85𝐸−14	1.461𝐸−13	2.362𝐸−13
4	14.83	28.01	154.9	1.540𝐸−13	9.27𝐸−14	5.232𝐸−13
5	126.8	236.3	1193	3.51𝐸−14	4.885𝐸−13	1.044𝐸−13
6	703.5	1373	6293	3.456𝐸−13	2.380𝐸−13	1.322𝐸−12
7	2910	6063	2.573𝑒+04	3.631𝐸−13	7.956𝐸−13	9.821𝐸−13
8	9790	2.174𝐸+04	8.736𝐸+04	3.341𝐸−13	1.257𝐸−12	1.942𝐸−12
9	2.827𝐸+04	6.649𝐸+04	2.570𝐸+05	1.135𝐸−12	5.373𝐸−13	3.824𝐸−12
10	7.263𝐸+04	1.795𝐸+05	6.751𝐸+05	1.881𝐸−13	2.688𝐸−12	1.640𝐸−13
11	1.700𝐸+05	4.386𝐸+05	1.617𝐸+06	1.667𝐸−12	1.403𝐸−12	7.308𝐸−12
12	3.687𝐸+05	9.877𝐸+05	3.587𝐸+06	2.270𝐸−12	4.234𝐸−12	6.352𝐸−12
13	7.510𝐸+05	2.078𝐸+06	7.464𝐸+06	1.822𝐸−12	5.436𝐸−12	6.050𝐸−12
14	1.450𝐸+06	4.130𝐸+06	1.470𝐸+07	3.771𝐸−12	2.083𝐸−12	1.348𝐸−11
15	2.675𝐸+06	7.813𝐸+06	2.763𝐸+07	1.679𝐸−12	1.232𝐸−11	1.565𝐸−12
16	4.741𝐸+06	1.417𝐸+07	4.983𝐸+07	7.809𝐸−12	4.950𝐸−12	1.999𝐸−11
17	8.117𝐸+06	2.475𝐸+07	8.667𝐸+07	1.510𝐸−12	7.840𝐸−12	1.008𝐸−11
18	1.348𝐸+07	4.184𝐸+07	1.460𝐸+08	2.601𝐸−12	9.133𝐸−12	1.983𝐸−11
19	2.177𝐸+07	6.870𝐸+07	2.391𝐸+08	9.656𝐸−12	5.884𝐸−12	3.032𝐸−11
20	3.431𝐸+07	1.099𝐸+08	3.817𝐸+08	5.291𝐸−12	4.470𝐸−12	1.424𝐸−11