On The Solution of Newell-Whitehead-Segel Equation

Mohand M. Abdelrahim Mahgoub; Abdelilah Kamal H. Sedeeg

doi:doi:10.11648/j.ajmcm.20160101.13

| Peer-Reviewed

On The Solution of Newell-Whitehead-Segel Equation

Mohand M. Abdelrahim Mahgoub, Abdelilah Kamal H. Sedeeg

Published in American Journal of Mathematical and Computer Modelling (Volume 1, Issue 1)

Received: 11 October 2016 Accepted: 19 October 2016 Published: 15 November 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper, we apply a combined form of the Elzaki transform method with the Adomian decomposition method to obtain the solution of Newell-Whitehead Segel equation. This method is called the Elzaki Adomian decomposition method (EADM). The method can be applied to linear and nonlinear problems. The result reveals that the proposed method is very efficient, simple and can be applied to linear and nonlinear problems.

Published in	American Journal of Mathematical and Computer Modelling (Volume 1, Issue 1)
DOI	10.11648/j.ajmcm.20160101.13
Page(s)	21-24
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Newell-Whitehead-Segel Equation, Elzaki Transform Method, Adomian Decomposition Method

References

[1]	A. M. Wazwaz, A First Course in Integral Equations, World Scientific, Singapore, 1997.
[2]	Q. Li, Z. Zheng, S. Wang, J. Liu, Lattice Bolzmann model for nonlinear heat equations, Adv. Neural Netw.(2012), 140-148.
[3]	A. Malik, F. Chand, H. Kumar, S. C. Mishra, Exact solutions of some physical models using the (G_ G) expansion method, Pramana J. Phys. 78 (4), (2012), 513-529.
[4]	A. Saravanan, N. Magesh, A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell-Whitehead-Segel equation, J. Egyptian Math. Soc, 21 (2013), 259-265.
[5]	S. A. Manaa, An Approximate solution to the Newell-Whitehead-Segel equation by the Adomian decomposition method, Raf. J. Comp. Math. 8 (1), (2011), 171-180.
[6]	Hassan Kamil Jassim, Homotopy perturbation algorithm using Laplace transform for Newell-Whitehead-Segel equation, Int. J. Adv. Appl. Math. And Mech. 2 (4) (2015) 8 - 12 (ISSN: 2347-2529).
[7]	P. Pue-on, Laplace Adomian Decomposition Method for Solving Newell-Whitehead-Segel Equation, Applied Mathematical Sciences, Vol. 7, 2013, no. 132, 6593 – 6600.
[8]	B. Malomed. The Newell-Whitehead-Segel equation for traveling waves. arXiv preprint patt-sol/9605001, 1996.
[9]	S. Nourazar, M. Soori, A. Nazari-Golshan. On the exact solution of Newell-Whitehead-Segel equation using the homotopy perturbation method. Journal of Applied Sciences Research, 2011, 7 (8).
[10]	A. Aasaraai. Analytic solution for Newell-Whitehead-Segel equation by differential transform method. Middle-East Journal of Scientific Research, 2011, 10 (2): 270–273.
[11]	R. Ezzati, K. Shakibi. Using Adomian’s decomposition and multiquadric quasi-interpolation methods for solving Newell-Whitehead equation. Procedia Computer Science, 2011, 3: 1043–1048.
[12]	J. Macıas-Dıaz, J. Ruiz-Ram´ırez. A non-standard symmetry-preserving method to compute bounded solutions of a generalized Newell-Whitehead-Segel equation. Applied Numerical Mathematics, 2011, 61 (4): 630–640.
[13]	Tarig M. Elzaki, (2011), The New Integral Transform “Elzaki Transform” Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 57-64.
[14]	Tarig M. Elzaki & Salih M. Elzaki, (2011), Application of New Transform “Elzaki Transform” to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 65-70.
[15]	. Abdelilah K. Hassan Sedeeg, and Mohand M. Abdelrahim Mahgob, Comparison of New Integral Transform "AboodhTransform" and Adomian Decomposition Method, International Journal of Mathematics And its Applications Volume 4, Issue 2 B (2016), 127-135.
[16]	Mohand M. Abdelrahim Mahgoub, “ On The Elzaki Transform of Heaviside Step Function with a Bulge Function,” IOSR Journal of Mathematics (IOSR-JM) Volume 11, Issue 2 Ver. III (Mar - Apr. 2015), PP 72-74.
[17]	Abdelbagy A. Alshikh and Mohand M. Abdelrahim Mahgoub, “A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform,” Pure and Applied Mathematics Journal 2016; 5 (5): 145-150.
[18]	Abdelbagy A. Alshikh and Mohand M. Abdelrahim Mahgoub, On The Relationship Between Elzaki Transform And New Integral Transform "ZZ Transform, International Journal of Development ResearchVol. 06, Issue, 08, pp. 9264-9270, August, 20231.
[19]	Tarig M. Elzaki & Salih M. Elzaki, (2011), On the Connections between Laplace and Elzaki transforms, Advances in Theoretical and Applied Mathematics, ISSN 0973-4554 Volume 6, Number 1, pp. 1-11.
[20]	G. Adomian. Solving frontier problems of physics: the decomposition method. Kluwer Boston, 1994.
[21]	A. M. Wazwaz, A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl Math Comput, 111 (1) (2000), 53-69.

Cite This Article

Plain Text BibTeX RIS

APA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah Kamal H. Sedeeg. (2016). On The Solution of Newell-Whitehead-Segel Equation. American Journal of Mathematical and Computer Modelling, 1(1), 21-24. https://doi.org/10.11648/j.ajmcm.20160101.13

Copy | Download

ACS Style

Mohand M. Abdelrahim Mahgoub; Abdelilah Kamal H. Sedeeg. On The Solution of Newell-Whitehead-Segel Equation. Am. J. Math. Comput. Model. 2016, 1(1), 21-24. doi: 10.11648/j.ajmcm.20160101.13

Copy | Download

AMA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah Kamal H. Sedeeg. On The Solution of Newell-Whitehead-Segel Equation. Am J Math Comput Model. 2016;1(1):21-24. doi: 10.11648/j.ajmcm.20160101.13

Copy | Download

@article{10.11648/j.ajmcm.20160101.13,
  author = {Mohand M. Abdelrahim Mahgoub and Abdelilah Kamal H. Sedeeg},
  title = {On The Solution of Newell-Whitehead-Segel Equation},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {1},
  number = {1},
  pages = {21-24},
  doi = {10.11648/j.ajmcm.20160101.13},
  url = {https://doi.org/10.11648/j.ajmcm.20160101.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20160101.13},
  abstract = {In this paper, we apply a combined form of the Elzaki transform method with the Adomian decomposition method to obtain the solution of Newell-Whitehead Segel equation. This method is called the Elzaki Adomian decomposition method (EADM). The method can be applied to linear and nonlinear problems. The result reveals that the proposed method is very efficient, simple and can be applied to linear and nonlinear problems.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - On The Solution of Newell-Whitehead-Segel Equation
AU  - Mohand M. Abdelrahim Mahgoub
AU  - Abdelilah Kamal H. Sedeeg
Y1  - 2016/11/15
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmcm.20160101.13
DO  - 10.11648/j.ajmcm.20160101.13
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 21
EP  - 24
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20160101.13
AB  - In this paper, we apply a combined form of the Elzaki transform method with the Adomian decomposition method to obtain the solution of Newell-Whitehead Segel equation. This method is called the Elzaki Adomian decomposition method (EADM). The method can be applied to linear and nonlinear problems. The result reveals that the proposed method is very efficient, simple and can be applied to linear and nonlinear problems.
VL  - 1
IS  - 1
ER  -

Copy | Download

Author Information

Mohand M. Abdelrahim Mahgoub

Department of Mathematics, Faculty of Science & Technology, Omdurman Islamic University, Khartoum, Sudan
Abdelilah Kamal H. Sedeeg

Mathematics Department, Faculty of Education, Holy Quran and Islamic Sciences University, Khartoum, Sudan

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah Kamal H. Sedeeg. (2016). On The Solution of Newell-Whitehead-Segel Equation. American Journal of Mathematical and Computer Modelling, 1(1), 21-24. https://doi.org/10.11648/j.ajmcm.20160101.13

Copy | Download

ACS Style

Mohand M. Abdelrahim Mahgoub; Abdelilah Kamal H. Sedeeg. On The Solution of Newell-Whitehead-Segel Equation. Am. J. Math. Comput. Model. 2016, 1(1), 21-24. doi: 10.11648/j.ajmcm.20160101.13

Copy | Download

AMA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah Kamal H. Sedeeg. On The Solution of Newell-Whitehead-Segel Equation. Am J Math Comput Model. 2016;1(1):21-24. doi: 10.11648/j.ajmcm.20160101.13

Copy | Download

@article{10.11648/j.ajmcm.20160101.13,
  author = {Mohand M. Abdelrahim Mahgoub and Abdelilah Kamal H. Sedeeg},
  title = {On The Solution of Newell-Whitehead-Segel Equation},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {1},
  number = {1},
  pages = {21-24},
  doi = {10.11648/j.ajmcm.20160101.13},
  url = {https://doi.org/10.11648/j.ajmcm.20160101.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20160101.13},
  abstract = {In this paper, we apply a combined form of the Elzaki transform method with the Adomian decomposition method to obtain the solution of Newell-Whitehead Segel equation. This method is called the Elzaki Adomian decomposition method (EADM). The method can be applied to linear and nonlinear problems. The result reveals that the proposed method is very efficient, simple and can be applied to linear and nonlinear problems.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - On The Solution of Newell-Whitehead-Segel Equation
AU  - Mohand M. Abdelrahim Mahgoub
AU  - Abdelilah Kamal H. Sedeeg
Y1  - 2016/11/15
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmcm.20160101.13
DO  - 10.11648/j.ajmcm.20160101.13
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 21
EP  - 24
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20160101.13
AB  - In this paper, we apply a combined form of the Elzaki transform method with the Adomian decomposition method to obtain the solution of Newell-Whitehead Segel equation. This method is called the Elzaki Adomian decomposition method (EADM). The method can be applied to linear and nonlinear problems. The result reveals that the proposed method is very efficient, simple and can be applied to linear and nonlinear problems.
VL  - 1
IS  - 1
ER  -

Copy | Download