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A New Approximate Analytical Method for ODEs Cover
Open Access
|Jul 2014

References

  1. NAYFEH, A. H. 2011. Introduction to perturbation techniques, Wiley-VCH.
  2. RAND, R. H., ARMBRUSTER, D. AND RAND, R. 1987. Perturbation methods, bifurcation theory and computer algebra, Springer-Verlag, New York.10.1007/978-1-4612-1060-3
  3. HE, J. H. 1999. Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering 178, 257-262.
  4. GANJI, D. D. 2006. The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Physics Letters A 355, 337-341.
  5. ABBASBANDY, S. 2006. Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method. Applied Mathematics and Computation 173, 493-500.
  6. YILDIRIM, A. AND KOCAK, H. 2009. Homotopy perturbation method for solving the space-time fractional advection-dispersion equation. Advances in Water Resources 32, 1711-1716.
  7. SHAKERI, F. AND DEHGHAN, M. 2008. Solution of delay differential equations via a homotopy perturbation method. Mathematical and Computer Modelling 48, 486-498.
  8. AMINIKHAH, H. 2010. An analytical approximation for solving nonlinear Blasius equation by NHPM. Numerical Methods for Partial Differential Equations 26, 1291-1299.
  9. AMINIKHAH, H. AND BIAZAR, J. 2009. A new HPM for ordinary differential equations. Numerical Methods for Partial Differential Equations 26, 480-489.
  10. BILDIK, N., KONURALP, A., ORAKCL, B. AND KUCUKARSLAN, S. 2006. Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method. Applied Mathematics and Computation 172, 551-567.
  11. BIAZAR, J., BABOLIAN, E. AND ISLAM, R. 2004. Solution of the system of ordinary differential equations by Adomian decomposition method. Applied Mathematics and Computation 147, 713-719.
  12. BABOLIAN, E., Biazar, J. AND Vahidi, A.R. 2004. Solution of a system of nonlinear equations by Adomian decomposition method. Applied Mathematics and Computation 150, 847-854.
  13. PAMUK, S. 2005. Solution of the porous media equation by Adomian's decomposition method. Physics Letters A 344, 184-188.
  14. LIAO, S. 2004. On the homotopy analysis method for nonlinear problems. Applied Mathematics andComputation 147, 499-513.
  15. ABBASBANDY, S. 2006. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Physics Letters A 360, 109-113.
  16. JAFARI, H. AND SEIFI, S. 2009. Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation. Communications in Nonlinear Science and Numerical Simulation 14, 2006-2012.
  17. ODIBAT, Z., MOMANI, S. AND ERTURK, S. 2008. Generalized differential transform method: Application to differential equations of fractional order. Applied Mathematics and Computation 197, 467-477.
  18. ERTURK, S. AND MOMANI, S. 2008. Solving systems of fractional differential equations using differential transform method. Journal of Computational and Applied Mathematics 215, 142-151.
  19. AYAZ, F. 2004. Solutions of the system of differential equations by differential transform method. Applied Mathematics and Computation 147, 547-567.
  20. GHORBANI, A. 2009. Beyond Adomian polynomials: He polynomials. Chaos, Solitons & Fractals 39, 14861492.
  21. SHAWAGFEH, N.T. 1993. Nonperturbative approximate solution for Lane-Emden equation. J. Math. Phys. 34, 4364-4369.
DOI: https://doi.org/10.2478/jamsi-2014-0002 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180
Language: English
Page range: 19 - 30
Published on: Jul 15, 2014
Published by: University of Ss. Cyril and Methodius in Trnava
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2014 Hossein Aminikhah, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.