Solution of burgers’ equation appears in fluid mechanics by multistage optimal homotopy asymptotic method

Author:

Wang Fuzhang1,Shah Ali2,Ahmad Imtiaz2,Ahmad Hijaz3,Alam Kamran4,Thounthong Phatiphat5

Affiliation:

1. College of Education, Nanchang Normal College of Applied Technology, Nanchang, China + Nanchang Institute of Technology, Nanchang, China + College of Mathematics, Huaibei Normal University, Huaibei, China

2. Department of Mathematics, University of Swabi, Swabi, Khyber Pakhtunkhwa, Pakistan

3. Operational Research Center in Healthcare, Near East University, Nicosia/Mersin, Turkey f Section of Mathematics, International Telematic University Uninettuno, Roma, Italy

4. Department of Pure and Applied Mathematics, The University of Haripur, Haripur, Pakistan

5. Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand

Abstract

In this article, we approximate analytical solution of Burgers? equations using the multistage homotopy asymptotic method which are utilized in modern physics and fluid mechanics. The suggested algorithm is an accurate and simple to-utilize semi-analytic tool for non-linear problems. In the current research we investigation the efficiency and accuracy of the method for the solution of non-linear PDE for large time span. Numerical comparison with the variational iteration method shows the efficacy and accuracy of the proposed method.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

Reference8 articles.

1. Cole, J. D., Perturbation Methods in Applied Mathematics, Blaisdell Publishing Company, Boston, Mass., USA, 1968

2. Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, Mass., USA, 1994

3. Liao, S. J., On the Homotopy Analysis Method for Non-Linear Problems, Appl. Math. Comput., 147 (2004), 2, pp. 499-513

4. Marinca, V., Herisanu, N., Application of Optimal Homotopy Asymptotic Method for Solving Non-Linear Equations Arising in Heat Transfer, Int. Commun. Heat Mass Transf., 35 (2008), 6, pp. 710-715

5. Alomari A. K., et al., The Homotopy Analysis Method for the Exact Solutions of the K(2,2), Burgers’ and Coupled Burgers Equations, Appl. Math. Sci., 2 (2008), 40, pp. 1963-1977

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