Advertisement

Erratum to: A New Approach for Numerical Solution of Modified Korteweg-de Vries Equation

  • Turgut Ak
  • S. Battal Gazi Karakoc
  • Anjan Biswas
Erratum
  • 219 Downloads

1 Erratum to: Iran J Sci Technol Trans Sci DOI 10.1007/s40995-017-0238-5

The original version of this article unfortunately contained mistakes. The presentation of Tables 2, 3 and 4 was incorrect. The corrected tables are given below.
Table 2

Invariants and error norms for single solitary wave with ε = 3, μ = 1, c = 0.845, h = 0.1, and ∆t = 0.01, 0 ≤ x ≤ 80

t

 

1

5

10

15

20

l 1

Present

4.442866

4.442866

4.442866

4.442866

4.442866

(Biswas and Raslan 2011)

4.443000

4.443138

4.444142

4.443420

4.443171

l 2

Present

3.676941

3.676941

3.676941

3.676941

3.676941

(Biswas and Raslan 2011)

3.677069

3.677535

3.678094

3.678642

3.679192

l 3

Present

2.072792

2.073533

2.073695

2.073772

2.073841

(Biswas and Raslan 2011)

2.073575

2.074357

2.075303

2.076232

2.077161

L 2-Error

Present

6.279015e−04

1.252048e−03

2.138787e−03

2.960441e−03

3.656694e−03

 

L -Error

Present

3.624348e−04

8.415234e−04

1.403498e−03

1.887116e−03

2.294197e−03

(Biswas and Raslan 2011)

1.206756e−03

3.621519e−03

5.942047e−03

7.626772e−03

8.642137e−03

Table 3

Comparison of invariants for the interaction of two solitary waves with ε = 3, μ = 1, h = 0.1, ∆t = 0.01, c 1 = 2, c 2 = 1, x 1 = 15 and x 2 = 25, 0 ≤ x ≤ 80

 

t

1

5

10

15

20

I 1

Present

8.885732

8.885732

8.885732

8.885732

8.885732

(Biswas and Raslan 2011)

8.886014

8.886776

8.889742

8.885983

8.884880

I 2

Present

9.659345

9.659345

9.659345

9.659345

9.659345

(Biswas and Raslan 2011)

9.659527

9.663714

9.662547

9.661071

9.661224

I 3

Present

10.270822

10.857214

10.954278

10.307099

10.338321

(Biswas and Raslan 2011)

10.239870

10.249000

10.246790

10.242580

10.242030

Table 4

Comparison of invariants for the interaction of three solitary waves with ε = 3, μ = 1, h = 0.1, ∆t = 0.01, c 1 = 2, c 2 = 1, c 3 = 0.5, x 1 = 15, x 2 = 25 and x 3 = 35, 0 ≤ x ≤ 80

 

t

1

5

10

15

20

I 1

Present

13.328677

13.328677

13.328677

13.328677

13.328677

(Biswas and Raslan 2011)

13.329060

13.330630

13.338780

13.332640

13.332060

I 2

Present

12.519943

12.519943

12.519943

12.519943

12.519943

(Biswas and Raslan 2011)

12.520280

12.526260

12.540860

12.526660

12.524900

I 3

Present

11.321178

13.483073

12.415348

12.413743

11.499146

(Biswas and Raslan 2011)

11.249790

11.261270

11.288040

11.259970

11.256730

Copyright information

© Shiraz University 2017

Authors and Affiliations

  • Turgut Ak
    • 1
  • S. Battal Gazi Karakoc
    • 2
  • Anjan Biswas
    • 3
    • 4
  1. 1.Department of Transportation Engineering, Faculty of EngineeringYalova UniversityYalovaTurkey
  2. 2.Department of Mathematics, Faculty of Science and ArtNevsehir Haci Bektas Veli UniversityNevsehirTurkey
  3. 3.Department of Mathematical SciencesDelaware State UniversityDoverUSA
  4. 4.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations