Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

Table 3

Numerical solution and absolute error of Example 3.

𝑥	Exact	𝜙10	|𝜙2−𝑦|	|𝜙4−𝑦|	|𝜙6−𝑦|
0.0	1.11022𝐸−16	0.00000𝐸−00	1.1102𝐸−16	1.1102𝐸−16	1.1102𝐸−16
0.1	−0.041435623	−0.041435620	5.2312𝐸−04	1.8827𝐸−05	9.0212𝐸−07
0.2	−0.073268382	−0.073268376	1.0017𝐸−03	3.6337𝐸−05	1.7458𝐸−06
0.3	−0.095799848	−0.095799840	1.3873𝐸−03	5.0792𝐸−05	2.4489𝐸−06
0.4	−0.109237721	−0.109237712	1.6377𝐸−03	6.0385𝐸−05	2.9199𝐸−06
0.5	−0.113703656	−0.113703646	1.7244𝐸−03	6.3752𝐸−05	3.0862𝐸−06
0.6	−0.109237721	−0.109237712	1.6377𝐸−03	6.0385𝐸−05	2.9199𝐸−06
0.7	−0.095799848	−0.095799840	1.3873𝐸−03	5.0792𝐸−05	2.4489𝐸−06
0.8	−0.073268382	−0.073268376	1.0017𝐸−03	3.6337𝐸−05	1.7458𝐸−06
0.9	−0.041435623	−0.041435620	5.2312𝐸−03	1.8827𝐸−05	9.0212𝐸−07
1.0	1.11022𝐸−16	2.88127𝐸−17	9.0205𝐸−17	1.3183𝐸−16	1.2533𝐸−16