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Table 2 Comparison of various iterations for \(\lambda =2\) and \(\alpha _{k}=\beta _{k}=0.9\) for \(k=0\) to 10

From: Numerical solution of Bratu’s boundary value problem based on Green’s function and a novel iterative scheme

t

Exact-Solution

Mann–Green

Ishikawa–Green

New

0.1

0.1144107440

1.04807 × 10−6

2.55453 × 10−9

2.42065 × 10−11

0.2

0.2064191156

2.00580 × 10−6

4.88750 × 10−9

4.63266 × 10−11

0.3

0.2738793116

2.77841 × 10−6

6.76865 × 10−9

6.41713 × 10−11

0.4

0.3150893646

3.28129 × 10−6

7.99268 × 10−9

7.57862 × 10−11

0.5

0.3289524214

3.45590 × 10−6

8.41760 × 10−9

7.98192 × 10−11

0.6

0.3150893646

3.28129 × 10−6

7.99268 × 10−9

7.57863 × 10−11

0.7

0.2738793116

2.77841 × 10−6

6.76865 × 10−9

6.41713 × 10−11

0.8

0.2064191156

2.00580 × 10−6

4.88750 × 10−9

4.63266 × 10−11

0.9

0.1144107440

1.04807 × 10−6

2.55453 × 10−9

2.42066 × 10−11