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Table 3 Influence of parameters: comparison of various iteration processes

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

Iterations

Values of λ

1.000

2.000

3.510

Comparison of the Absolute errors when t = 0.1

DM [7]

2.7 × 10−3

1.6 × 10−21

6.1 × 10−19

LDM [26]

2.0 × 10−6

2.6 × 10−3

6.1 × 10−19

B-Spline [27]

3.0 × 10−6

1.7 × 10−5

3.8 × 10−2

LGSM [28]

7.5 × 10−7

4.0 × 10−6

4.4 × 10−5

Spline [29]

5.8 × 10−10

9.7 × 10−9

6.6 × 10−6

DTM [30]

1.3 × 10−6

GVM [31]

4.2 × 10−12

7.6 × 10−12

9.3 × 10−9

CW [32]

1.2 × 10−19

2.0 × 10−18

2.3 × 10−10

Our Scheme

3.2 × 10−15

5.2 × 10−15

4.1 × 10−15

Comparison of the Absolute errors when t = 0.4

DM [7]

2.2 × 10−3

3.3 × 10−3

LDM [26]

7.7 × 10−6

8.0 × 10−3

B-Spline [27]

8.5 × 10−6

5.3 × 10−5

1.2 × 10−1

LGSM [28]

5.2 × 10−7

3.1 × 10−6

4.4 × 10−7

Spline [29]

9.6 × 10−11

2.4 × 10−8

6.8 × 10−6

DTM [30]

2.0 × 10−10

4.9 × 10−6

GVM [31]

2.1 × 10−11

4.4 × 10−11

3.0 × 10−8

CW [32]

7.8 × 10−19

5.4 × 10−17

1.1 × 10−9

Our Scheme

1.2 × 10−14

2.2 × 10−15

3.1 × 10−15

Comparison of the Absolute errors when t = 0.6

DM [7]

2.2 × 10−3

3.2 × 10−3

LDM [26]

1.1 × 10−5

3.3 × 10−2

B-Spline [27]

8.4 × 10−6

5.3 × 10−6

1.3 × 10−1

LGSM [28]

5.1 × 10−9

3.1 × 10−6

4.5 × 10−5

Spline [29]

9.6 × 10−11

2.4 × 10−8

6.8 × 10−6

DTM [30]

2.0 × 10−10

6.7 × 10−6

GVM [31]

3.2 × 10−11

6.4 × 10−11

3.1 × 10−8

CW [32]

7.9 × 10−19

5.5 × 10−17

1.2 × 10−9

Our Scheme

4.2 × 10−16

6.2 × 10−16

4.4 × 10−16

Comparison of the Absolute errors when t = 0.9

DM [7]

2.7 × 10−3

1.5 × 10−2

LDM [26]

1.2 × 10−5

1.5 × 10−2

B-Spline [27]

3.0 × 10−6

1.7 × 10−5

3.8 × 10−2

LGSM [28]

7.4 × 10−7

4.0 × 10−6

4.4 × 10−5

Spline [29]

5.8 × 10−10

9.7 × 10−9

6.6 × 10−6

DTM [30]

2.0 × 10−10

7.4 × 10−6

GVM [31]

4.7 × 10−11

8.4 × 10−11

1.1 × 10−8

CW [32]

1.2 × 10−19

2.0 × 10−18

2.3 × 10−10

Our Scheme

4.3 × 10−15

4.7 × 10−16

5.3 × 10−16