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

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.

scholarly journals On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
E. E. Eladdad ◽  
E. A. Tarif
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In the current work, a combination between a new integral transform and the homotopy perturbation method is presented. This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations.

scholarly journals Approximate analytical solution for Phi-four equation with he’s fractal derivative

2021 ◽  
pp. 127-127
Author(s):  
Shuxian Deng ◽  
Xinxin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Integral Transform ◽  
Approximate Analytical Solution ◽  
Homotopy Perturbation ◽  
Fractal Derivative ◽  
Fractal Differential Equations ◽  
First Time

This paper, for the first time ever, proposes a Laplace-like integral transform, which is called as He-Laplace transform, its basic properties are elucidated. The homotopy perturbation method coupled with this new transform becomes much effective in solving fractal differential equations. Phi-four equation with He?s derivative is used as an example to reveal the main merits of the present technology.

HOMOTOPY PERTURBATION METHOD AND PARAMETERIZED PERTURBATION METHOD FOR RADIUS OF CURVATURE BEAM EQUATION

2012 ◽  
Vol 01 (04) ◽  
pp. 1250033 ◽  
Author(s):  
S. S. SAMAEE ◽  
O. YAZDANPANAH ◽  
D. D. GANJI
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillations ◽  
Nonlinear Partial Differential Equations ◽  
Beam Equation ◽  
Radius Of Curvature ◽  
Strongly Nonlinear ◽  
Homotopy Perturbation ◽  
Strongly Nonlinear Oscillations ◽  
Parameterized Perturbation Method

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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