[PDF] Top 20 Application of He's homotopy perturbation method for solving Sivashinsky equation

... In the solidification of dilute binary alloy, a planar solid-liquid interface is often found to be unsta- ble, spontaneously assuming a cellular structure. This situation enables one to derive on asymptotic nonlinear ... See full document

... the homotopy perturbation method was combined with the He’s polynomials and well-known Laplace transformation method (Madan & Fathizadeh, 2010) to produce a highly effective algorithm and ... See full document

... integral equation, is a known analytic function, and are linear and nonlinear functions of ...the equation (1) turn out to be a classical Fredholm integro- differential ... See full document

... Riccati equation plays a great role in blueprint and analysis the linear and nonlinear optimal control ...this equation has been acquired by applying Adomian’s decomposition method [1], ... See full document

... paper, homotopy perturbation method is applied to solve moving boundary and isoperimetric ...This method does not depend upon a small parameter in the equation, homotopy is ... See full document

... differential equation of the first order, following this by chapters on the Riccati equation (as a bridge between linear and nonlinear equations) and existence theorems, with special reference to Cauchy's ... See full document

... this method, the time interval is divided into n equal subintervals and the method is applied once to each ...Riccati equation by the homo- topy perturbation method [1], the iterated ... See full document

... the homotopy perturbation Sumudu transform method (HPSTM) is extended to solve linear and nonlinear fractional Klein-Gordon ...the method, some examples are ...novel application of ... See full document

... 4]. He [5-20] developed the variational iteration and homotopy perturbation methods for solving linear, nonlinear, initial and boundary value ...Moreover, He realized the physical ... See full document

... new method proposed by some au- thors new for solving optimal control problem based on Pontryagin’s maximum principle or Hamilton-Jacobi- Bellman equation, such as the relaxed descent method, ... See full document

... homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact ...differential equation oscillations have crucial ... See full document

... and homotopy perturbation method to solve homogeneous and nonhomogeneous nonlinear partial differential ...This method solves nonlinear partial differential equations without applying ... See full document

... the homotopy perturbation method (HPM) [1-23], variational iteration method (VIM) and Adomian decomposition method (ADM) ...By application of standard homotopy and ... See full document

... where A is a general differential operator, f (r) is a known analytic function, B is a boundary operator, u is the unknown function, and Γ is the boundary of the domain Ω. The operator A can be generally divided into two ... See full document

... the homotopy perturbation Sumudu transform method (HPSTM) to solve li- near and nonlinear fractional Klein-Gordon ...the method, some examples are ...novel application of ... See full document

... The homotopy perturbation method (HPM) was first proposed by the Chinese mathematician Ji-Huan He ...the homotopy perturbation method leads to an analytical approximate ... See full document

... diffusion equation by a differential quadrature method” ...J.H. He, 2003 “ Homotopy perturbation method: A new nonlinear ... See full document

... The homotopy analysis method is developed in 1992 by Liao ...other perturbation methods is that this method is independent of small/large physical ...This method has been successfully ... See full document

... tensively studied over a number of years and successfully developed by numerous authors (e.g. [7-26] to mention only a few). As well known, this method is a combina- tion of homotopy in topology and classic ... See full document

... [7] Ghorbani, A. and Saberi-Nadjafi, J. (2007) He’s Homotopy Perturbation Method for Calculating Adomian Polynomials. International Journal of Nonlinear Sciences and Numerical Simulation , 8, ... See full document