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

Table 5

Numerical solution and absolute error of Example 3 for different 𝑁 values.

Present method
𝑥	Exact solution	𝑦8	𝐸8	𝑦10	𝐸10	𝑦20	𝐸20
0.0	1.386294	1.386294	0.00000000	1.386294	0.00000000	1.386294	0.1200𝐸−17
0.1	1.410987	1.410833	0.15424𝐸−4	1.410833	0.15424𝐸−4	1.410833	0.15424𝐸−4
0.2	1.435085	1.434461	0.62350𝐸−4	1.434461	0.62350𝐸−4	1.434461	0.62350𝐸−4
0.3	1.458615	1.457198	0.14110𝐸−3	1.457198	0.14165𝐸−3	1.457198	0.14165𝐸−3
0.4	1.481605	1.479064	0.25409𝐸−3	1.479064	0.25409𝐸−3	1.479064	0.25409𝐸−3
0.5	1.504077	1.500007	0.40029𝐸−3	1.500007	0.40029𝐸−3	1.500074	0.40029𝐸−3
0.6	1.526056	1.520248	0.58081𝐸−3	1.520248	0.58081𝐸−3	1.526056	0.58081𝐸−3
0.7	1.547563	1.539602	0.79609𝐸−3	1.539602	0.79609𝐸−3	1.547563	0.79609𝐸−3
0.8	1.568616	1.558151	0.10465𝐸−2	1.558151	0.10465𝐸−2	1.568616	0.10465𝐸−2
0.9	1.589235	1.575911	0.13324𝐸−2	1.575911	0.13324𝐸−2	1.589235	0.13324𝐸−2
1.0	1.609438	1.592899	0.16540𝐸−2	1.592899	0.16539𝐸−2	1.609438	0.16539𝐸−2