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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 857612, 7 pages
Homotopy Perturbation Method with an Auxiliary Term
1National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, China
2Modern Textile Institute, Donghua University, Shanghai 200051, China
Received 2 October 2011; Accepted 17 November 2011
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Ji-Huan He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [28 citations]
The following is the list of published articles that have cited the current article.
- Hossein Yahyazadeh, Davood Domairry Ganji, Arash Yahyazadeh, Mohammad Taghi Khalili, Payam Jalili, and Mohsen Jouya, “Evaluation Of Natural Convection Flow Of A Nanofluid Over A Linearly Stretching Sheet In The Presence Of Magnetic Field By The Differential Transformation Method,” Thermal Science, vol. 16, no. 5, pp. 1281–1287, 2012.
- Y. Y. Lee, “Analysis of the Nonlinear Structural-Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods,” Abstract and Applied Analysis, vol. 2012, pp. 1–13, 2012.
- Hasibun Naher, and Farah Aini Abdullah, “New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the -Dimensional Evolution Equation,” Journal of Applied Mathematics, vol. 2012, pp. 1–18, 2012.
- Muhammad Asif Zahoor Raja, Junaid Ali Khan, Siraj-ul-Islam Ahmad, and Ijaz Mansoor Qureshi, “A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence,” Computational Intelligence and Neuroscience, vol. 2012, pp. 1–10, 2012.
- Asma Ali Elbeleze, Adem Kiliçman, and Bachok M. Taib, “Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order,” Abstract and Applied Analysis, vol. 2012, pp. 1–14, 2012.
- Ji-Huan He, “Asymptotic Methods for Solitary Solutions and Compactons,” Abstract and Applied Analysis, vol. 2012, pp. 1–130, 2012.
- H. Saberi Najafi, and S.A. Edalatpanah, “Homotopy Perturbation Method for Linear Programming Problems,” Applied Mathematical Modelling, 2013.
- A. R. Vahidi, Z. Azimzadeh, and M. Didgar, “An efficient method for solving Riccati equation using homotopy perturbation method,” Indian Journal Of Physics, vol. 87, no. 5, pp. 447–454, 2013.
- Hamid M. Sedighi, Kourosh H. Shirazi, and Mohammad A. Attarzadeh, “A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches,” Acta Astronautica, vol. 91, pp. 245–250, 2013.
- M. A. Abdelkawy, A. H. Bhrawy, and M. M. Tharwat, “Integrable system modelling shallow water waves: Kaup-Boussinesq shallow water system,” Indian Journal Of Physics, vol. 87, no. 7, pp. 665–671, 2013.
- H. Vázquez-Leal, Y. Khan, A. L. Herrera-May, U. Filobello-Nino, A. Sarmiento-Reyes, V. M. Jiménez-Fernández, D. Pereyra-Díaz, A. Perez-Sesma, R. Castaneda-Sheissa, A. Díaz-Sanchez, and J. Huerta-Chua, “Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum,” Mathematical Problems in Engineering, vol. 2013, pp. 1–12, 2013.
- Abdon Atangana, and Dumitru Baleanu, “Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations within Sumudu Transform,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013.
- Ali Akgül, Adem Kılıçman, and Mustafa Inc, “Improved ()-Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations,” Abstract and Applied Analysis, vol. 2013, pp. 1–7, 2013.
- Lan Xu, and Eric W. M. Lee, “Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet,” Abstract and Applied Analysis, vol. 2013, pp. 1–5, 2013.
- Ihsan Timuçin Dolapçi, Mehmet Senol, and Mehmet Pakdemirli, “New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations,” Journal of Applied Mathematics, vol. 2013, pp. 1–5, 2013.
- Hector Vazquez-Leal, Yasir Khan, Uriel Filobello-Nino, Arturo Sarmiento-Reyes, Alejandro Diaz-Sanchez, and Luis-F. Cisneros-Sinencio, “Fixed-Term Homotopy,” Journal of Applied Mathematics, vol. 2013, pp. 1–11, 2013.
- Xiang Hong, Jun Wang, and Li-xin Lu, “Application of Homotopy Perturbation Method with an Auxiliary Term for Nonlinear Dropping Equations Arisen in Polymer Packaging System,” Mathematical Problems in Engineering, vol. 2013, pp. 1–5, 2013.
- Hasibun Naher, Farah Aini Abdullah, and Syed Tauseef Mohyud-Din, “Extended generalized Riccati equation mapping method for the fifth-order Sawada-Kotera equation,” AIP Advances, vol. 3, no. 5, pp. 052104, 2013.
- Hong-Yan Liu, Ji-Huan He, and Zheng-Biao Li, “Fractional calculus for nanoscale flow and heat transfer,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24, no. 6, pp. 1227–1250, 2014.
- R. Nouri, D.D. Ganji, and M. Hatami, “Unsteady sedimentation analysis of spherical particles in Newtonian fluid media using analytical methods,” Propulsion and Power Research, 2014.
- S.S. Samaee, O. Yazdanpanah, D.D. Ganji, and A.A. Mofidi, “Analytical solution for a suspension bridge by applying HPM and VIM,” International Journal of Computer Mathematics, pp. 1–20, 2014.
- J. H. He, “Homotopy perturbation method with two expanding parameters,” Indian Journal of Physics, vol. 88, no. 2, pp. 193–196, 2014.
- Ji-Huan He, “A Tutorial Review on Fractal Spacetime and Fractional Calculus,” International Journal of Theoretical Physics, vol. 53, no. 11, pp. 3698–3718, 2014.
- Mehmet Şenol, and I. Timuçin Dolapci, “On the Perturbation-Iteration Algorithm for Fractional Differential Equations,” Journal of King Saud University - Science, 2015.
- K. Sayevand, and H. Jafari, “On systems of nonlinear equations: some modified iteration formulas by homotopy perturbation method with accelerated fourth- and fifth-order convergence,” Applied Mathematical Modelling, 2015.
- Selva Balaji Munusamy, and Anirban Dhar, “Homotopy Perturbation Method-Based Analytical Solution for Tide-Induced Groundwater Fluctuations,” Groundwater, 2015.
- Muhammad Suleman, and Qingbiao Wu, “Comparative Solution of Nonlinear Quintic Cubic Oscillator Using Modified Homotopy Perturbation Method,” Advances in Mathematical Physics, vol. 2015, pp. 1–5, 2015.
- Soheil Ganjefar, and Sara Rezaei, “A modified homotopy perturbation method for optimal control problems using Pade approximant,” Applied Mathematical Modelling, 2016.