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Open Engineering

formerly Central European Journal of Engineering

Editor-in-Chief: Ritter, William

1 Issue per year


CiteScore 2017: 0.70

SCImago Journal Rank (SJR) 2017: 0.211
Source Normalized Impact per Paper (SNIP) 2017: 0.787

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Online
ISSN
2391-5439
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The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients

Abdul-Majid Wazwaz
Published Online: 2014-03-15 | DOI: https://doi.org/10.2478/s13531-013-0141-6

Abstract

We apply the variational iteration method (VIM) for solving linear and nonlinear ordinary differential equations with variable coefficients. We use distinct Lagrange multiplier for each order of ODE. We emphasize the power of the method by testing a variety of models with distinct orders and variable coefficients. Scientific models, namely, the hybrid selection model, the Thomas-Fermi equation, the Kidder equation of the Unsteady flow of gas through a porous medium, and the Riccati equation, are studied as well.

Keywords: Variational iteration method; Thomas-Fermi equation; hybrid model; Kidder equation

  • [1] A. M. Wazwaz, The variational iteration method for analytic treatment for linear and nonlinear ODEs, Appl. Math. Comput., 212(1) (2009) 120–134. http://dx.doi.org/10.1016/j.amc.2009.02.003CrossrefGoogle Scholar

  • [2] A.M. Wazwaz, The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation, Appl. Math. Comput., 105 (1999) 11–19. http://dx.doi.org/10.1016/S0096-3003(98)10090-5CrossrefGoogle Scholar

  • [3] A.M. Wazwaz, The modified decomposition method applied to unsteady flow of gas through a porous medium, Applied Mathematics and Computation, 118(2/3) (2001) 123–132. http://dx.doi.org/10.1016/S0096-3003(99)00209-XCrossrefGoogle Scholar

  • [4] J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. math. Comput., 114(2/3) (2000) 115–123. http://dx.doi.org/10.1016/S0096-3003(99)00104-6Web of ScienceCrossrefGoogle Scholar

  • [5] J.H. He, Variational iteration method — Some recent results and new interpretations, J. Comput. Appl. Math., 207(1) (2007) 3–17. http://dx.doi.org/10.1016/j.cam.2006.07.009CrossrefGoogle Scholar

  • [6] H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, (1962). Google Scholar

  • [7] H. Carslaw and J. Jaeger, Conduction of Heat in Solids, Oxford, London (1947). Google Scholar

  • [8] R. C. Roberts, Unsteady flow of gas through a porous medium Proceedings of the first U.S National Congress of Applied Mechanics, Ann Arbor, Mich., 773–776 (1952). Google Scholar

  • [9] R. E. Kidder, Unsteady flow of gas through a semiinfinite porous medium, Journal of Applied Mechanics, 27 (1067) 329–332. Google Scholar

About the article

Published Online: 2014-03-15

Published in Print: 2014-03-01


Citation Information: Open Engineering, Volume 4, Issue 1, Pages 64–71, ISSN (Online) 2391-5439, DOI: https://doi.org/10.2478/s13531-013-0141-6.

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© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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