A New Approximate Analytical Method for ODEs

NAYFEH, A. H. 2011. Introduction to perturbation techniques, Wiley-VCH.Search in Google Scholar

RAND, R. H., ARMBRUSTER, D. AND RAND, R. 1987. Perturbation methods, bifurcation theory and computer algebra, Springer-Verlag, New York.10.1007/978-1-4612-1060-3Search in Google Scholar

HE, J. H. 1999. Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering 178, 257-262.Search in Google Scholar

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.Search in Google Scholar

ABBASBANDY, S. 2006. Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method. Applied Mathematics and Computation 173, 493-500.Search in Google Scholar

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.Search in Google Scholar

SHAKERI, F. AND DEHGHAN, M. 2008. Solution of delay differential equations via a homotopy perturbation method. Mathematical and Computer Modelling 48, 486-498.Search in Google Scholar

AMINIKHAH, H. 2010. An analytical approximation for solving nonlinear Blasius equation by NHPM. Numerical Methods for Partial Differential Equations 26, 1291-1299.Search in Google Scholar

AMINIKHAH, H. AND BIAZAR, J. 2009. A new HPM for ordinary differential equations. Numerical Methods for Partial Differential Equations 26, 480-489.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

PAMUK, S. 2005. Solution of the porous media equation by Adomian's decomposition method. Physics Letters A 344, 184-188.Search in Google Scholar

LIAO, S. 2004. On the homotopy analysis method for nonlinear problems. Applied Mathematics andComputation 147, 499-513.Search in Google Scholar

ABBASBANDY, S. 2006. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Physics Letters A 360, 109-113.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

AYAZ, F. 2004. Solutions of the system of differential equations by differential transform method. Applied Mathematics and Computation 147, 547-567.Search in Google Scholar

GHORBANI, A. 2009. Beyond Adomian polynomials: He polynomials. Chaos, Solitons & Fractals 39, 14861492.Search in Google Scholar

SHAWAGFEH, N.T. 1993. Nonperturbative approximate solution for Lane-Emden equation. J. Math. Phys. 34, 4364-4369.Search in Google Scholar