An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique

Bolujo Joseph Adegboyegun

doi:doi:10.11648/j.pamj.20130203.14

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An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique

Bolujo Joseph Adegboyegun

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 3)

Received: 23 June 2013 Published: 10 July 2013

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Abstract

In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 3)
DOI	10.11648/j.pamj.20130203.14
Page(s)	134-139
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), 2013. Published by Science Publishing Group

Keywords

Burger’s Equation, Homotopy Perturbation Method, Adomian Decomposition Method

References

[1]	L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Second ed., Birkauser, Broston, 2004.
[2]	Cole J.D, On a quasilinear parabolic equation occurring in aerodynamics, Quart. Appl. Math., 9 pp 225-236
[3]	Benton et al, A table of solution of the one dimensional Burgers’ equation, Quart, Appl. Math., 30, pp 195-212
[4]	B.B Sangi et al, A Fourier method for the solution of the nonlinear advection problem, Appl. Math., (14) (1988), 385-389
[5]	MiralBhaget et al (2013), Explicit solution of Burgers’ and generalized Burgers’ equation usingHomotopy perturbation method. IJAET.Vol.,6, issue 1, pp 179-188
[6]	Varoglu et al, Space B time finite elements incorporating characteristics for Burgers’ equation,Int. J. Num. Math. Eng., 16 pp 171-184
[7]	Alksan, E.N., A.A. Zdes, and T.A-Zis, (1972), A numerical solution of Burgers’ equation based on least squares approximation. AppliedMath. Comput., 176, pp 270-279
[8]	Caldwell J., Wanless P, and Cook A.E (1981), A finite element approach to Burger’s equation, Applied Math-Model, 5, pp 189-193
[9]	M. HadiRafiee et al (2013), Approximate solution to Burgers’ equation using reconstruction of Variational iteration method. Appl., Math. 2013, 3 (2): 45-49
[10]	G. Adomian, Solving frontier problems of physics. The Decomposition Method. Kluer,Boston; 1994
[11]	Wazwaz A.M, A new algorithm for calculating Adomian polynomials for nonlinearoperators, Appl. Math Comp 2000; 11: 35-51
[12]	G. Adomian, A review of the decomposition method in applied mathematics. J. Math Anal Appl. 1988; 135:501-544
[13]	Adomian, G. and Rach, R. (1983b), "Nonlinear stochastic operators", Journal of Mathematical Analysis and Applications, vol. 91, no. 2, pp. 94-10
[14]	B.J Adegboyegun and E.A Ibijola. (2012), A Comparison of Adomian’s DecompositionMethod and Picard Iteration Method In Solving Non-linear Differential Equations. Global Journals Inc. (US), Vol. 12 Issue 7; 1 (2012): 37-42.

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Bolujo Joseph Adegboyegun. (2013). An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique. Pure and Applied Mathematics Journal, 2(3), 134-139. https://doi.org/10.11648/j.pamj.20130203.14

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Bolujo Joseph Adegboyegun. An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique. Pure Appl. Math. J. 2013, 2(3), 134-139. doi: 10.11648/j.pamj.20130203.14

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AMA Style

Bolujo Joseph Adegboyegun. An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique. Pure Appl Math J. 2013;2(3):134-139. doi: 10.11648/j.pamj.20130203.14

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@article{10.11648/j.pamj.20130203.14,
  author = {Bolujo Joseph Adegboyegun},
  title = {An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {3},
  pages = {134-139},
  doi = {10.11648/j.pamj.20130203.14},
  url = {https://doi.org/10.11648/j.pamj.20130203.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130203.14},
  abstract = {In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity   does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while  .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.},
 year = {2013}
}

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TY  - JOUR
T1  - An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique
AU  - Bolujo Joseph Adegboyegun
Y1  - 2013/07/10
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130203.14
DO  - 10.11648/j.pamj.20130203.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 134
EP  - 139
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130203.14
AB  - In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity   does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while  .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.
VL  - 2
IS  - 3
ER  -

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Author Information

Bolujo Joseph Adegboyegun

School of Mathematics and applied Statistics, Faculty of Informatics, University of Wollongong, Australia

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APA Style

Bolujo Joseph Adegboyegun. (2013). An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique. Pure and Applied Mathematics Journal, 2(3), 134-139. https://doi.org/10.11648/j.pamj.20130203.14

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ACS Style

Bolujo Joseph Adegboyegun. An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique. Pure Appl. Math. J. 2013, 2(3), 134-139. doi: 10.11648/j.pamj.20130203.14

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AMA Style

Bolujo Joseph Adegboyegun. An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique. Pure Appl Math J. 2013;2(3):134-139. doi: 10.11648/j.pamj.20130203.14

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@article{10.11648/j.pamj.20130203.14,
  author = {Bolujo Joseph Adegboyegun},
  title = {An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {3},
  pages = {134-139},
  doi = {10.11648/j.pamj.20130203.14},
  url = {https://doi.org/10.11648/j.pamj.20130203.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130203.14},
  abstract = {In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity   does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while  .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique
AU  - Bolujo Joseph Adegboyegun
Y1  - 2013/07/10
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130203.14
DO  - 10.11648/j.pamj.20130203.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 134
EP  - 139
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130203.14
AB  - In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity   does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while  .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.
VL  - 2
IS  - 3
ER  -

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