Numerical Solution For Time-Delay Burgers Equation By Homotopy Analysis Method
DOI:
https://doi.org/10.32792/jeps.v11i2.129الملخص
In this paper, the homotopy analysis method(HAM) has been applied for solving time-delay Burgers equation. HAM contains the auxiliary parameter ћ, which provides us with a simple way to control the convergence region of solution series. In this study, we compare obtained results through HAM with the exact solutions to show the accuracy of HAM
المراجع
References
A. S. Bataineh, M. S. M. Noorani, and I. Hashim, Direct solution of n-th order IVPs by Homotopy analysis method, Diff. Eq. and Nonlinear Mech., Doi: 10.1155/2009/842094.
A. K. Alomari, M. S. M. Noorani and R. Nazar, The Homotopy analysis method for the exact solutions of the K(2,2),Burgers and coupled burgers equations, Appl. Math. Sci.2(40)(2008) 1963-1977.
A. Adawi and F. Awawdeh, a numerical method for solving linear integral equations, Int. J. Contemp. Math. Sciences 4(10)(2009)485-496.
A. Sami Bataineh, M. S. M. Noorani and I. Hashim, Approximate solutions of singular two-point BVPs by modified Homotopy analysis method, Phy. Lett. A 372(2008) 4062-4066.
A. El-Nahhas, Analytical approximations for Thomas-Fremi equation, Acta Physica Polonica A 114(4)(2008) 913-1116.
A. El-Ajou, Z. Odibat, S. Momani and A. Alawneh, Construction of analytical solutions to fractional differential equations using Homotopy analysis method, IAENG Int. J. Appl. Math. 40:2, IJAM-40-2-01.
A. R. Abd-Ellateef Kamar, Monotone iteration technique for singular perturbation problem, Appl. Math. Comp. 131 (2002) 559-571.
E. S. Fahmy, H. A. Abdusalam, K. R. Raslan, On the solutions of the time-delayed Burgers equation, Nonlinear Analysis 69 (2008) 4775-4786.
E. S. Fahmy,Travelling wave solutions for some time-delayed equations through factorizations, Chaos, Solitons & Fractals 38 (2008) 1209-1216.
E. S. Fahmy,Travelling wave solutions for some time-delayed equations through factorizations, Chaos, Solitons & Fractals 38 (2008) 1209-1216.
F. Awawdeh, H. M. Jaradat and O. Alsayyed, Solving system of DAEs by Homotopy analysis method, Chaos, Solitons and Fractals 42(2009)1422-1427.
F. Geng, M.Cui. B. Zhang, Method for solving nonlinear initial value problems by combining Homotopy perturbation and reproducing kernel Hilbert space methods, Nonlinear Analysis: Real World Applications 11 (2010) 637-644.
G. M. Abd El-Latif, Ahomotopy technique and a perturbation technique for non-linear problems, Appl. Math. Comp. 169 (2005) 576-588.
G. Domairry, M. Ghanbarpour and F. Ghanbarpour, Homotopy analysis method of three dimensional diffusion equations, J. Appl. Math. 10(1)(2009) 45-61.
G. M. Abd El-Latif, Ahomotopy technique and a perturbation technique for non-linear problems, Appl. Math. Comp. 169 (2005) 576-588.
H. Kim, R. Sakthivel, Travelling wave solutions for time-delayed nonlinear evolution equations, Appl. Math. Lett. 23 (2010) 527-532.
H. Jafari, C. Chun, S. Seifi and M. Saeidy, Analytical solution for nonlinear Gas dynamic equation by Homotopy analysis method,Appl. Appl. Math. 4(1)(2009) 149-154.
H. Jafari, M. Saeidy and J. Vahidi, the Homotopy analysis method for solving fuzzy system of linear equation, Int. J. of fuzzy sys. 11(4)(2009)308-313.
H. Jafari and M. A. Firoozjaee, Homotopy analysis method for solving KDV equations, Surveys in Math. and it's Appl. 5(2010) 89-98.
H. H. Zadeh, H. Jafari and S. M. Karimi, Homotopy analysis method for solving integral and integro-differential equations, IJRRAS 2(2)(2010) 140-144.
H. Kim, R. Sakthivel, Travelling wave solutions for time-delayed nonlinear evolution equations, Appl. Math. Lett. 23 (2010) 527-532.
J.H. He, Homotopy perturbation technique, Comput. Math. Appl. Mech. Eng. 178 (3-4) (1999) 257-262.
J.H. He, Homotopy perturbation method: a new nonlinear analytical technique for nonlinear problems, Appl. Math. Comput. 135(2003) 73-79.
J.H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Nonlinear Mech. 35(2000) 37-43.
J. Saberi, A.Ghorbani, He's homotopy perturbation method: An effective tool for solving nonlinear integral and integro-differential equations, Comp. Math. Appl. 58(2009) 2379-2390.
J. Biazar, H. Ghazvini, Convergence of the homotopy perturbation method for partial differential equations, Nonlinear Analysis: Real World Applications 10 (2009) 2633-2640.
M. Matinfar and M. Saeidy, Application of Homotopy analysis method for solving to fourth-order parabolic partial differential equations, Appl. Appl. Math. 5(1)(2010) 70-80.
M. Ghasemi, M. T. Kajani, A. Davari, Numerical solution of two-dimensional nonlinear differential equation by homotopy perturbation method, Appl. Math. Comp. 189 (2007) 341-345.
M. A. Noor, S. T. Mhyod-Din, Homotopy perturbation method for solving sixth-order boundary value problems, Comp.Math.Appl. 55 (2008) 2953-2972.
N. Smaoui, M. Mekkaoui, The generalized Burgers equation with and without a time delay, J. Appl. Math. and Stoch. Anal. 1(2004) 73-96.
N. Smaoui, M. Mekkaoui, The generalized Burgers equation with and without a time delay, J. Appl. Math. and Stoch. Anal. 1(2004) 73-96.
O. Abdulaziz, I. Hashim and A. Saif, Series solutions of time-fractional PDEs by Homotopy analysis method, Diff. Eq. Nonl. Mech., Doi: 10.1155/2008/686512.
S. Liao, On the Homotopy analysis method for nonlinear problems, Appl. Math. Comp.147(2004)499-513.
S. Liao, Comparison between the Homotopy analysis method and Homotopy perturbation method, Appl. Math. Comp. 169(2005) 1186-1194.
Shu-Li Mei, Sen-Wen Zhang, Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations,Comp.Math. Appl.54 (2007) 1092-1100.
Z. Abbas, S. Vahdati, F. Ismail and A. K. Dizicheh, Application of Homotopy analysis method for linear integro-differential equations, Int. Math. Forum 5(5)(2010) 237-249.
التنزيلات
منشور
إصدار
القسم
الرخصة
The Authors understand that, the copyright of the articles shall be assigned to Journal of education for Pure Science (JEPS), University of Thi-Qar as publisher of the journal.
Copyright encompasses exclusive rights to reproduce and deliver the article in all form and media, including reprints, photographs, microfilms and any other similar reproductions, as well as translations. The reproduction of any part of this journal, its storage in databases and its transmission by any form or media, such as electronic, electrostatic and mechanical copies, photocopies, recordings, magnetic media, etc. , will be allowed only with a written permission from Journal of education for Pure Science (JEPS), University of Thi-Qar.
Journal of education for Pure Science (JEPS), University of Thi-Qar, the Editors and the Advisory International Editorial Board make every effort to ensure that no wrong or misleading data, opinions or statements be published in the journal. In any way, the contents of the articles and advertisements published in the Journal of education for Pure Science (JEPS), University of Thi-Qar are sole and exclusive responsibility of their respective authors and advertisers.