Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

Table 1

Numerical results of Example 1 for 𝛼=1.

𝑡	Exact solution	Absolute error in [22]	Absolute error in [20]	LWM	LWM	LWM
				𝑀=2, 𝑘=2	𝑀=3, 𝑘=2	𝑀=5, 𝑘=3
0.1	0.099667	7.51𝐸−09	9.30𝐸−05	0	0	0
0.2	0.197375	1.52𝐸−06	2.93𝐸−02	1.91𝐸−08	0	0
0.3	0.291312	3.93𝐸−05	3.78𝐸−03	2.72𝐸−08	1.45𝐸−13	0
0.4	0.379948	4.32𝐸−04	2.81𝐸−03	1.65𝐸−08	1.17𝐸−13	1.94𝐸−16
0.5	0.462117	8.41𝐸−04	9.80𝐸−04	1.31𝐸−08	3.28𝐸−13	3.20𝐸−16
0.6	0.537049	2.94𝐸−05	7.93𝐸−03	1.98𝐸−08	4.97𝐸−13	1.24𝐸−16
0.7	0.604367	3.35𝐸−04	9.44𝐸−03	2.52𝐸−08	6.32𝐸−13	1.58𝐸−16
0.8	0.664036	5.44𝐸−04	1.17𝐸−02	2.94𝐸−08	7.36𝐸−13	1.84𝐸−16
0.9	0.716297	6.56𝐸−09	3.96𝐸−02	3.23𝐸−08	8.12𝐸−13	1.94𝐸−16
1.0	0.761594	2.53𝐸−06	2.95𝐸−02	2.63𝐸−08	4.62𝐸−13	1.99𝐸−16