Archive
Special Issues

Volume 2, Issue 3, June 2013, Page: 134-139
An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique
Bolujo Joseph Adegboyegun, School of Mathematics and applied Statistics, Faculty of Informatics, University of Wollongong, Australia
Received: Jun. 23, 2013;       Published: Jul. 10, 2013
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.
Keywords
Burger’s Equation, Homotopy Perturbation Method, Adomian Decomposition Method
Bolujo Joseph Adegboyegun, An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique, Pure and Applied Mathematics Journal. Vol. 2, No. 3, 2013, pp. 134-139. doi: 10.11648/j.pamj.20130203.14
Reference
[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.