Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations

Mei, Shuli; Zhang, Sen-Wen

doi:10.1016/j.camwa.2006.12.074

Cited by 19 publications

(15 citation statements)

References 30 publications

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“…Using this approach the approximate analytic solution is obtained. In [40] solved the nonlinear matrix differential equations by homotopy perturbation method. A dynamic system and Burgers equation are taken as examples to illustrate its effectiveness and convenience.…”

Section: The Homotopy Perturbation Methodsmentioning

confidence: 99%

He's homotopy perturbation method for solving Korteweg‐de Vries Burgers equation with initial condition

İnç

2010

Numerical Methods Partial

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In this article, we present the Homotopy Perturbation Method (Shortly HPM) for obtaining the numerical solutions of the Korteweg-de Vries Burgers (KdVB) equation. The series solutions are developed and the reccurance relations are given explicity. The initial approximation can be freely chosen with possibly unknown constants which can be determined by imposing the boundary and initial conditions. The results reveal that HPM is very simple and effective.

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Section: The Homotopy Perturbation Methodsmentioning

confidence: 99%

He's homotopy perturbation method for solving Korteweg‐de Vries Burgers equation with initial condition

İnç

2010

Numerical Methods Partial

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“…Mei and Zhang [32] developed a coupling technique of He's VIM and HPM to give an approximate analytic solution of the nonlinear matrix differential equations. In this algorithm, the correct functional is developed [13][14][15][33][34][35][36] and the Lagrange multipliers are calculated optimally via variational theory.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity

et al. 2012

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The coupling of the homotopy perturbation method (HPM) and the variational iteration method (VIM) is a strong technique for solving higher dimensional initial boundary value problems. In this article, after a brief explanation of the mentioned method, the coupled techniques are applied to one-dimensional heat transfer in a rectangular radial fin with a temperature-dependent thermal conductivity to show the effectiveness and accuracy of the method in comparison with other methods. The graphical results show the best agreement of the three methods; however, the amount of calculations of each iteration for the combination of HPM and VIM was reduced markedly for multiple iterations. It was found that the variation of the dimensionless temperature strongly depends on the dimensionless small parameter ε 1 . Moreover, as the dimensionless length increases, the thermal conductivity of the fin decreases along the fin.

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“…But the traditional perturbation method requires the presence of a small parameter which is not so with the solution obtained using the homotopy perturbation method . Authors of [24] solved the nonlinear matrix differential equations by homotopy perturbation method . A dynamic system and Burgers equation are taken as examples to illustrate its effectiveness and convenience.…”

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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Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations

Cited by 19 publications

References 30 publications

He's homotopy perturbation method for solving Korteweg‐de Vries Burgers equation with initial condition

He's homotopy perturbation method for solving Korteweg‐de Vries Burgers equation with initial condition

An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity

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

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