A New Piecewise-Spectral Homotopy Analysis Method for Solving Chaotic Systems of Initial Value Problems

Table 1

Numerical comparison between PSHAM and ode45 for the Genesio-Tesi system.

𝑡	𝑦1(𝑡)		𝑦2(𝑡)		𝑦3(𝑡)
	PSHAM	ode45	PSHAM	ode45	PSHAM	ode45
10	0.549279	0.549279	−0.794566	−0.794566	−2.165635	−2.165635
20	5.582458	5.582458	−0.637436	−0.637436	−8.466611	−8.466611
30	−1.358402	−1.358402	1.702324	1.702324	7.595114	7.595114
40	−0.234737	−0.234737	−5.138959	−5.138959	1.042740	1.042740
50	5.405530	5.405530	0.923128	0.923128	−9.945397	−9.945397
60	−1.416682	−1.416682	−0.050327	−0.050327	7.152612	7.152612
70	0.709463	0.709463	−5.405633	−5.405633	−0.694185	−0.694185