Application of He's homotopy-perturbation method to strongly nonlinear coupled systems

In this paper, homotopy perturbation method (HPM) and parameterized perturbation method (PPM) are used to solve the radius of curvature beam equation. This paper compares the HPM and PPM in order to solve the equations of curvature beam. A comparative study between the HPM, PPM and numerical method (NM) is presented in this work. The validity of our solutions is verified by the numerical results. The achieved results reveal that the HPM and PPM are very effective, convenient and quite accurate to nonlinear partial differential equations. These methods can be easily extended to other strongly nonlinear oscillations and can be found widely applicable in engineering and science.

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A New Modification of The HPM for The Duffing Equation With High Nonlinearity

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v2i2.2099 ◽

2013 ◽

Vol 2 (2) ◽

pp. 124-133

Author(s):

Ahmed Khdir

Keyword(s):

Perturbation Method ◽

Spectral Methods ◽

Homotopy Perturbation Method ◽

Numerical Solutions ◽

High Accuracy ◽

Duffing Equation ◽

Nonlinear Ordinary Differential Equations ◽

Strongly Nonlinear ◽

Homotopy Perturbation ◽

Pseudo Spectral

In this work we introduce a new modification of the homotopy perturbation method for solving nonlinear ordinary differential equations. The technique is based on the blending of the Chebyshev pseudo-spectral methods and the homotopy perturbation method (HPM). The method is tested by solving the strongly nonlinear Duffing equation for undamped oscillators. Comparison is made between the proposed technique, the standard HPM, an earlier modification of the HPM and the numerical solutions to demonstrate the high accuracy, applicability and validity of the present approach.

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Homotopy perturbation method for the solution of the electrostatic potential differential equation

Mathematical Problems in Engineering ◽

10.1155/mpe/2006/83878 ◽

2006 ◽

Vol 2006 ◽

pp. 1-6 ◽

Cited By ~ 18

Author(s):

Li-Na Zhang ◽

Ji-Huan He

Keyword(s):

Differential Equation ◽

Perturbation Method ◽

Homotopy Perturbation Method ◽

Nonlinear Problems ◽

Strongly Nonlinear ◽

Homotopy Perturbation ◽

Explicit Analytical Solution ◽

Approximate Analytical Solutions ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

This paper obtains an explicit analytical solution for nonlinear Poisson-Boltzmann equation by the homotopy perturbation method, which does not require a small parameter in the equation under study, so it can be applied to both the weakly and strongly nonlinear problems. The obtained results show the evidence of the usefulness of the homotopy perturbation method for obtaining approximate analytical solutions for nonlinear equations.

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Study of strongly nonlinear oscillators using the Aboodh transform and the homotopy perturbation method

The European Physical Journal Plus ◽

10.1140/epjp/i2019-12824-6 ◽

2019 ◽

Vol 134 (9) ◽

Cited By ~ 2

Author(s):

K. Manimegalai ◽

Sagar Zephania C F ◽

P. K. Bera ◽

P. Bera ◽

S. K. Das ◽

...

Keyword(s):

Perturbation Method ◽

Homotopy Perturbation Method ◽

Nonlinear Oscillators ◽

Strongly Nonlinear ◽

Homotopy Perturbation ◽

Strongly Nonlinear Oscillators

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Combination of Kharrat-Toma Transform and Homotopy Perturbation Method to Solve a Strongly Nonlinear Oscillators Equation.

JOURNAL OF SCIENCE, COMPUTING AND ENGINEERING RESEARCH ◽

10.46379/jscer.2021.020102 ◽

2020 ◽

pp. 143-146

Author(s):

Bachir Nour Kharrat ◽

George Albert Toma

Keyword(s):

Perturbation Method ◽

Homotopy Perturbation Method ◽

Integral Transform ◽

Physical Sciences ◽

Restoring Force ◽

Strongly Nonlinear ◽

Homotopy Perturbation ◽

Modified Method ◽

Force Equation ◽

Strongly Nonlinear Oscillators

This article introduces a new hybridization between the Kharrat-Toma transform and the homotopy perturbation method for solving a strongly nonlinear oscillator with a cubic and harmonic restoring force equation that arising in the applications of physical sciences. The proposed method is based on applying our new integral transform "Kharrat-Toma Transform" and then using the homotopy perturbation method. The objective of this paper is to illustrate the efficiency of this hybrid method and suggestion modified it. The results showed that the modified method is effectiveness and more accurate.

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