Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations

Table 5

Higher order oscillation equation: comparison of solutions by the Haar wavelet-quasilinearization technique at 6th iteration and level of resolutions 𝐽=10 with generalized differential quadrature rule (GDQR) method [14] and exact solution.

𝛼=4
6th iteration				𝐽=10
𝑥	𝑦Exact [14]	𝑦GDQR [14]	𝐸GDQR [14]	𝑦HAAR	𝐸HAAR
0.0	0	0	0	0	0
0.7	1.2692	1.2693	−0.002	1.2692	0.0025
1.4	2.0990	2.0993	−0.010	2.0990	0.0037
2.1	2.0929	2.0933	−0.019	2.0928	0.0048
2.8	1.2541	1.2545	−0.027	1.2541	0.0059
3.5	−0.0179	−0.0177	0.813	−0.0179	−0.1679
4.2	−1.2843	−1.2842	0.003	−1.2843	−0.0010
4.9	1.0880	−2.1051	−0.004	1.0879	0.0063
5.6	−2.0866	−2.0868	−0.014	−2.0865	−0.0046
6.3	−1.2390	−1.2395	−0.039	−1.2389	−0.0083
7.0	0.0357	0.0352	1.276	0.0358	0.2095
7.7	1.2992	1.2990	0.013	1.2992	0.0010
8.4	2.1109	2.1111	−0.009	2.1108	0.0031
9.1	2.0801	2.0805	−0.021	2.0800	0.0056
9.8	1.2237	1.2243	−0.044	1.2236	0.0099
10.5	−0.0536	−0.0529	1.146	−0.0537	−0.1965
11.2	−1.3141	−1.3136	0.037	−1.3141	−0.0042
11.9	−2.1166	−2.1166	−0.002	−2.1166	−0.0022
12.6	−2.0734	−2.0741	−0.030	−2.0733	−0.0068
13.3	−1.2084	−1.2093	−0.071	−1.2082	−0.0136
14.0	0.0714	0.0706	1.057	0.0715	0.1888