Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations

Table 4

Force-free Duffing-Van der Pol Oscillator Equation: comparison of solutions by the Haar wavelet-quasilinearization technique 𝑦_HAAR at 5th iteration and level of resolutions 𝐽=9 with decomposition method 𝑦_ADM [13] and numerical solution based on the fourth-order Runge-Kutta.

𝛼=2
5th iteration			𝐽=9
𝑥	𝑦RK	𝑦ADM [13]	𝑦HAAR	Absolute Error
0.0	2.00000	1.99750	2.00000	2.1e − 12
0.1	1.98971	1.98724	1.98971	1.7e − 7
0.2	1.95936	1.95697	1.95936	3.5e − 7
0.3	1.90980	1.90758	1.90980	5.4e − 7
0.4	1.84202	1.84008	1.84202	7.3e − 7
0.5	1.75702	1.75552	1.75702	9.2e − 7
0.6	1.65586	1.65493	1.65586	1.1e − 6
0.7	1.53958	1.53937	1.53958	1.3e − 6
0.8	1.40923	1.53937	1.40923	1.4e − 6
0.9	1.26586	1.26726	1.26586	1.6e − 6
1.0	1.11054	1.11267	1.11054	1.7e − 6
1.1	0.94435	0.94704	0.94435	1.9e − 6
1.2	0.76846	0.77147	0.76846	2.0e − 6
1.3	0.58411	0.58715	0.58410	2.1e − 6
1.4	0.39267	0.39545	0.39267	2.3e − 6
1.5	0.19567	0.19795	0.19566	2.4e − 6