Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

Table 1

Numerical result of Example 15 compared with the Taylor polynomial solution and Tau-Chebyshev and Legendre method.

𝑥𝑖	Exact solution	RKHS method	Taylor polynomial	Tau-Chebyshev	Tau-Legendre
−1.0	0.36787944	0.36787943	0.36787911	0.36787942	0.36787942
−0.8	0.44932896	0.44932895	0.44932892	0.44932896	0.44932896
−0.6	0.54881164	0.54881164	0.54881163	0.54881164	0.54881164
−0.4	0.67032005	0.67032005	0.67032005	0.67032004	0.67032004
−0.2	0.81873075	0.81873075	0.81873076	0.81873075	0.81873075
0.00	1	1	1	1	1
0.20	1.22140276	1.22140276	1.22140277	1.22140276	1.22140276
0.40	1.49182470	1.49182472	1.49182482	1.49182469	1.49182469
0.60	1.82211880	1.82211881	1.82211942	1.82211880	1.82211880
0.80	2.22554093	2.22554093	2.22554335	2.22554092	2.22554092
1.00	2.71828183	2.71828182	2.71828972	2.71828180	2.71828181