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Theory and Modern Applications

Table 1 Picard iterations

From: A solution to nonlinear Fredholm integral equations in the context of w-distances

\(x_{n}\)

\(x_{0}= 0.25\)

\(x_{0}= 0.5\)

\(x_{0}= 0.75\)

\(x_{0} =1\)

\(x_{1}\)

1.5625e−02

6.2500e−02

1.4062e−01

2.5000e−01

\(x_{2}\)

6.1035e−05

9.7656e−04

4.9438e−03

1.5625e−02

\(x_{3}\)

9.3132e−10

2.3842e−07

6.1104e−06

6.1035e−05

\(x_{4}\)

2.1684e−19

1.4211e−14

9.3343e−12

9.3132e−10

\(x_{5}\)

1.1755e−38

5.0487e−29

2.1782e−23

2.1684e−19

\(x_{6}\)

3.4545e−77

6.3724e−58

1.1862e−46

1.1755e−38

\(x_{7}\)

2.9833e−154

1.0152e−115

3.5174e−93

3.4545e−77

\(x_{8}\)

2.2251e−308

2.5765e−231

3.0930e−186

2.9833e−154

\(x_{9}\)

0

0

0

2.2251e−308

\(x_{10}\)

0

0

0

0