Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials

Table 3

Numerical results of Example 3 for 𝛼=4 and 𝛼=3.75.

𝑥𝑖	𝛼=3.75
	LCM for 𝑁=13	PM for 𝑁=10	GDTM for 𝑁=13
0.0	1.00000000	1.00000000	1.00000000
0.1	1.10618147	1.10618610	1.10617705
0.2	1.22328484	1.22329275	1.22327680
0.3	1.35238877	1.35239964	1.35237837
0.4	1.49473312	1.49474546	1.49472145
0.5	1.65172131	1.65173324	1.65170946
0.6	1.82492929	1.82494001	1.82491846
0.7	2.01611828	2.01612731	2.01610929
0.8	2.22724889	2.22725546	2.22714245
0.9	2.46049864	2.46050202	2.46049530
1.0	2.71828183	2.71828183	2.71828183
𝑥𝑖	𝛼=4
	LCM for 𝑁=13	PM for 𝑁=9	Exact solution
0.0	1.00000000	1.00000000	1.00000000
0.1	1.10517092	1.10517092	1.10517092
0.2	1.22140276	1.22140276	1.22140276
0.3	1.34985881	1.34985881	1.34985881
0.4	1.49182470	1.49182470	1.49182470
0.5	1.64872127	1.64872127	1.64872127
0.6	1.82211880	1.82211880	1.82211880
0.7	2.01375271	2.01375271	2.01375271
0.8	2.22554093	2.22554093	2.22554093
0.9	2.45960311	2.45960311	2.45960311
1.0	2.71828183	2.71828183	2.71828183