Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method

Table 1

Approximate solutions for Example 1.

𝑡	𝑥	𝛼=1/3		𝛼=1/2		𝛼=2/3		𝛼=1
		𝑢HPM	𝑢LEG	𝑢HPM	𝑢LEG	𝑢HPM	𝑢LEG	𝑢HPM	𝑢LEG	𝑢EX
0.0	0.25	0.25	0.25	0.25	0.25	0.25	0.25	0.25	0.25	0.25
	0.50	0.50	0.50	0.50	0.50	0.50	0.50	0.50	0.50	0.50
	0.75	0.75	0.75	0.75	0.75	0.75	0.75	0.75	0.75	0.75
	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
0.25	0.25	0.95546	0.93263	0.81419	0.78225	0.68960	0.66479	0.50	0.50	0.50
	0.50	1.20546	1.18263	1.06419	1.03225	0.93960	0.91479	0.75	0.75	0.75
	0.75	1.45546	1.43263	1.31419	1.28225	1.18960	1.16479	1.00	1.00	1.00
	1.00	1.70546	1.68263	1.56419	1.53225	1.43960	1.41479	1.25	1.25	1.25
0.50	0.25	1.13882	1.30877	1.04788	1.13276	0.94783	0.98312	0.75	0.75	0.75
	0.50	1.38882	1.55877	1.29788	1.38276	1.19783	1.23312	1.00	1.00	1.00
	0.75	1.63882	1.80877	1.54788	1.63276	1.44783	1.48312	1.25	1.25	1.25
	1.00	1.88882	2.05877	1.79788	1.88276	1.69783	1.73312	1.50	1.50	1.50
0.75	0.25	1.26745	1.37843	1.22721	1.30152	1.16441	1.20499	1.00	1.00	1.00
	0.50	1.51745	1.62843	1.47721	1.55152	1.41441	1.45499	1.25	1.25	1.25
	0.75	1.76745	1.87843	1.72721	1.80152	1.66441	1.70499	1.50	1.50	1.50
	1.00	2.01745	2.12843	1.97721	2.05152	1.91441	1.95499	1.75	1.75	1.75
1.00	0.25	1.36985	1.14160	1.37838	1.28854	1.35773	1.33039	1.25	1.25	1.25
	0.50	1.61985	1.39160	1.62838	1.53854	1.60773	1.58039	1.50	1.50	1.50
	0.75	1.86985	1.64160	1.87838	1.78854	1.85773	1.83039	1.75	1.75	1.75
	1.00	2.11985	1.89160	2.12838	2.03854	2.10773	2.08039	2.00	2.00	2.00