Explicit Solutions of Helmholtz Equation and Fifth-order KdV Equation using Homotopy Perturbation Method

By M. Rafei, D. Domiri Ganji. 2006

224 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e386daf6cd5bd57b14c95e9a0ea3a0d9321483de

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Citations in the corpus

Application of He's Homotopy Perturbation Method to Sumudu Transform (2007, methodology): “[17], to nonlinear oscillator by Cai [18], and to compute the Laplace transform by Abbasbandy [19].”
Modified homotopy perturbation method for solving non-linear Fredholm integral equations (2009, background): “[10]; for the thin film flow of a fourth grade fluid down a vertical cylinder by Siddiqui et al.”
He's Homotopy Perturbation Method for Calculating Adomian Polynomials (2007, background): “Homotopy perturbation method(HPM)[l-10] proposed by Ji-Huan He has been recently intensively studied by scientists and engineers and used for solving various nonlinear problems [11-18], The method has been shown to solve effectively, easily, and accurately a large class of nonlinear problems, genera”
Explicit analytical solutions of the generalized Burger and Burger–Fisher equations by homotopy perturbation method (2009, background): “For example, it was applied to the quadratic Ricatti differential equation by Abbasbandy [17], to the axisymmetric flow over a stretching sheet by Ariel et al. [18], to the nonlinear systems of reaction–diffusion equations by Ganji and Sadighi [19], to the Helmholtz equation and fifth-order KdV equa”
Exp-function Method for the Discrete mKdV Lattice (2007, background): “c2w„ = (a-u(2)n)(un+] -«„_,) (2) There are many approaches to searching for various solitonary solutions for nonlinear differential equations, such as the homotopy perturbation method[3-9], the variational iteration methods[10-16], and the parameter-expanding method[17], A review on recently develop”
Application of He's Homotopy-perturbation Method to Nonlinear Coupled Systems of Reaction-diffusion Equations (2006, methodology): “HPM was successfully applied to nonlinear oscillators with discontinuities [19], boundary value problems [23], heat radiation equations [24], generalized Hirota-Satsuma coupled KdV equation [25], Helmholtz Equation and Fifth-order KdV Equation [33].”
Exp-function Method for the Hybrid-Lattice System (2007, methodology): “In the past decades, several powerful methods have been developed to construct many types of exact solutions of nonlinear partial differential equations(PDEs), such as the tanh function method[l,2], Jacobian elliptic function method[3], the homotopy perturbation method[4-7], and the variational iter”
Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators (2013, methodology): “The explicit solution for the Helmholtz equationwas considered in [5] by using the homotopy perturbation method.”