Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments

Table 6

Numerical solution of Example 4 for different 𝑁 values.

Present method and corrected Laguerre polynomial solution
𝑥	Exact solution	𝑦12	𝑦12,15	𝑦22	𝑦22,28	𝑦25	𝑦25,28
0.0	1.000000	0.999999	1.000000	0.999999	1.000000	1.000000	1.000000
0.1	0.995004	0.996593	0.996600	0.996593	0.993964	0.996593	0.993963
0.2	0.980067	0.986641	0.986365	0.986641	0.975909	0.986641	0.975909
0.3	0.955336	0.969544	0.969444	0.969544	0.946004	0.969544	0.946003
0.4	0.921061	0.946139	0.946036	0.946139	0.904531	0.946139	0.904529
0.5	0.877583	0.916382	0.916381	0.916382	0.851886	0.916382	0.851884
0.6	0.825336	0.880504	0.880768	0.880504	0.788573	0.880504	0.788570
0.7	0.764842	0.838776	0.839522	0.838776	0.715199	0.838776	0.715195
0.8	0.696707	0.791509	0.793010	0.791509	0.632466	0.791509	0.632461
0.9	0.621610	0.739046	0.741629	0.739046	0.541167	0.739046	0.541161
1.0	0.540302	0.681764	0.685810	0.681764	0.442174	0.681764	0.442167