Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

Table 2

Numerical solution and absolute error of Example 2.

𝑥	Exact	𝜙10	|𝜙2−𝑦|	|𝜙4−𝑦|	Error [5]
0.0	0.000000000	0.000000000	0.0000𝐸−00	0.0000𝐸−00	0.0000𝐸−00
0.1	0.099833417	0.099833417	5.3658𝐸−09	8.7652𝐸−14	3.3266𝐸−04
0.2	0.198669331	0.198669331	6.7508𝐸−07	1.7463𝐸−10	1.5351𝐸−03
0.3	0.295520207	0.295520207	1.1207𝐸−05	1.4393𝐸−08	6.6505𝐸−03
0.4	0.389418342	0.389418342	8.0648𝐸−05	3.1851𝐸−07	1.3901𝐸−02
0.5	0.479425539	0.479425539	3.6516𝐸−04	3.3996𝐸−06	2.4222𝐸−02
0.6	0.564642473	0.564642473	1.2282𝐸−03	2.2720𝐸−05	4.6982𝐸−02
0.7	0.644217687	0.644217683	3.3532𝐸−03	1.0927𝐸−04	6.8954𝐸−02
0.8	0.717356091	0.717356031	7.8338𝐸−03	4.1109𝐸−04	9.5915𝐸−02
0.9	0.783326910	0.783326286	1.6204𝐸−02	1.2762𝐸−03	1.4380𝐸−01
1.0	0.841470985	0.841466258	3.0377𝐸−02	3.3927𝐸−03	1.8538𝐸−01