A coupling method of a homotopy technique and a perturbation technique for non-linear problems

He, Ji‐Huan

doi:10.1016/s0020-7462(98)00085-7

Cited by 1,535 publications

(898 citation statements)

References 2 publications

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“…Homptopy perturbation method was first proposed by the Chinese mathematician He [16][17][18][19][20]. This method has been employed to solve a large variety of linear and nonlinear problems such as fractional partial differential equations [32], the nonlinear HirotaSatsuma coupled KdV partial differential equation [12], nonlinear boundary value problems [22], traveling wave solutions of nonlinear wave equations [21], Nonlinear convective-radiative cooling equation, nonlinear heat equation (porous media equation) and nonlinear heat equation with cubic nonlinearity [13], the Newton-like iteration methods for solving non-linear equations or improving the existing iteration methods [9], evaluating the efficiency of straight fins with temperature-dependent thermal conductivity and determining the temperature distribution within the fin [26], the inverse parabolic equations and computing an unknown time-dependent parameter [28], finding improved approximate solutions to conservative truly nonlinear oscillators [4], complicated integrals which cannot be expressed in terms of elementary functions or analytical formulae [10] and etc.…”

Section: The Homotopy Perturbation Methodsmentioning

confidence: 99%

Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields Using He's Homotopy Perturbation Method

Dehghan¹,

Shakeri²

2008

PIER

203

108

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Abstract-In this research, an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy perturbation method (HPM) is used for solving this equation. HPM is an analytical procedure for finding the solutions of problems which is based on the constructing a homotopy with an imbedding parameter p that is considered as a small parameter. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity and efficiency of this method.

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Section: The Homotopy Perturbation Methodsmentioning

confidence: 99%

Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields Using He's Homotopy Perturbation Method

Dehghan¹,

Shakeri²

2008

PIER

203

108

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“…(o, y) = erf 1 2 2 y e y 2 / 2 + e y 2 / 2 (27) Again, to find the solution of this equation by HPM, we simply take the equation in an operator form as…”

Section: Fokker-planck Equation In Plasma Physicsmentioning

confidence: 99%

Application of Homotopy Perturbation Method in Nonlinear Heat Diffusion-Convection-Reaction Equations

Tolou¹,

Ganji²,

Hosseini³

et al. 2007

TOMECHJ

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Abstract:In this Paper, Homotopy-Perturbation method (HPM) which is one of the most recent approximate analytical solutions is implemented to solve diffusion-convection-reaction equations (DCRE). The calculations are carried out for two different types of DCRE's such as the Black-Scholes equation used in financial market option pricing and FokkerPlanck equation from plasma physics. The behavior of the approximate solutions of the distribution functions are shown graphically and are compared with those obtained by other theories (e.g. the Adomian decomposition method, ADM). It shows that the numerical results of these methods are the same; while HPM is much easier, more convenient and more efficient than ADM.

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“…Homotopy is an important part of topology [7] and it can convert any non-linear problem in to a finite linear problems and it doesn't depend on small parameter (see [2,3,5] ).…”

Section: Introductionmentioning

confidence: 99%

New Homotopy Perturbation Method To Solve Non-linear Problems

Rabbani¹

2013

J. Math. Computer Sci.

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In this article, we introduce a new homotopy perturbation method (NHPM) for solving non-linear problems, such that it can be converted a non-linear differential equations to some simple linear differential. We will solve linear differential equation by using analytic method that it is better than the variational iteration method and to find parameter , we use projection method, which is easier and decrease computations in comparison with similar works. Also in some of the references perturbation method are depend on small parameter but in our proposed method it is not depend on small parameter, finally we will solve some example for illustrating validity and applicability of the proposed method.

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A coupling method of a homotopy technique and a perturbation technique for non-linear problems

Cited by 1,535 publications

References 2 publications

Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields Using He's Homotopy Perturbation Method

Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields Using He's Homotopy Perturbation Method

Application of Homotopy Perturbation Method in Nonlinear Heat Diffusion-Convection-Reaction Equations

New Homotopy Perturbation Method To Solve Non-linear Problems

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