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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 [27 citations]
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- 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.
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- 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.
- 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.
- 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.
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- 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.
- 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.
- 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.
- 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.
- 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.
- Mehmet Şenol, and I. Timuçin Dolapci, “On the Perturbation-Iteration Algorithm for Fractional Differential Equations,” Journal of King Saud University - Science, 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.