Homotopy perturbation method: a new nonlinear analytical technique

He, Ji‐Huan

doi:10.1016/s0096-3003(01)00312-5

Cited by 1,236 publications

(671 citation statements)

References 8 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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“…(15) and (16) with the help of HPM, we construct the following equation (Abbasbandy 2006;He 2003;Wazwaz 2002):…”

Section: Solution Of the Problemmentioning

confidence: 99%

The mathematical analysis for peristaltic flow of nano fluid in a curved channel with compliant walls

Nadeem

Maraj

2012

Appl Nanosci

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In the present paper, we have investigated the peristaltic flow of nano fluid in a curved channel with compliant walls. The governing equations of nano fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified using the long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity, temperature, nano particle volume fraction and stream functions.

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“…In addition, several groups demonstrated the efficiency and suitability of the HPM for solving nonlinear equations and other electrochemical problems [26][27][28][29]. He [30] used HPM to solve the Lighthill equation, the Duffing equation [31], and the Blasius equation [32]. This method has also been used to solve nonlinear boundary value problems [33], integral equation [34][35][36], Klein-Gordon and Sine-Gordon equations [37], Emden-Flower-type equations [38], and several other problems [39][40][41].…”

Section: For Small and Medium Values Of The Saturation Parameter α Anmentioning

confidence: 99%

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

Anitha¹,

Alwarappan

Rajendran³

2012

ISRN Physical Chemistry

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A theoretical model of reaction/diffusion within conducting polymer microelectrodes is discussed. The model is based on the steady-state diffusion equation containing a nonlinear term related to the Michaelis-Menten kinetic of the enzymatic reaction. An analytical expression pertaining to the concentration of substrate and current is obtained using homotopy perturbation method for all values of diffusion and the saturation parameter. The substrate concentration profile and current response can be used in a large range of concentrations including the non-linear contributions. These approximate analytical results were found to be in good agreement with the previously reported limiting case results.

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Homotopy perturbation method: a new nonlinear analytical technique

Cited by 1,236 publications

References 8 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

The mathematical analysis for peristaltic flow of nano fluid in a curved channel with compliant walls

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

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