scholarly journals Li–He’s modified homotopy perturbation method coupled with the energy method for the dropping shock response of a tangent nonlinear packaging system

2020 ◽  
pp. 146134842091445
Author(s):  
Qiu-Ping Ji ◽  
Jun Wang ◽  
Li-Xin Lu ◽  
Chang-Feng Ge
Keyword(s):  
Perturbation Method ◽  
Energy Method ◽  
Homotopy Perturbation Method ◽  
Packaging System ◽  
Homotopy Perturbation ◽  
System A ◽  
Runge Kutta Method ◽  
Accuracy Comparison ◽  
Shock Response ◽  
Maximal Displacement

This paper couples Li–He’s homotopy perturbation method with the energy method to obtain an approximate solution of a tangent nonlinear packaging system. A higher order homotopy equation is constructed by adopting the basic idea of the Li–He’s homotopy perturbation method. The energy method is used to improve the maximal displacement and the frequency of the system to an ever higher accuracy. Comparison with the numerical solution obtained by the Runge–Kutta method shows that the shock responses of the system solved by the new method are more effective with a relative error of 0.15%.

scholarly journals Application of Homotopy Perturbation Method with an Auxiliary Term for Nonlinear Dropping Equations Arisen in Polymer Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xiang Hong ◽  
Jun Wang ◽  
Li-xin Lu
Keyword(s):  
Numerical Simulation ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Equation Of Motion ◽  
High Accuracy ◽  
Second Order ◽  
Packaging System ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions

The homotopy perturbation method (HPM) with an auxiliary term was applied to obtain approximate analytical solutions of polymer cushioning packaging system. The second-order solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this modified HPM with convenient calculation.

scholarly journals Assessment of homotopy perturbation method in nonlinear convective-radiative non-Fourier conduction heat transfer equation with variable coefficient

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 263-274 ◽  
Author(s):  
Mohsen Torabi ◽  
Hessameddin Yaghoobi ◽  
Seyfolah Saedodin
Keyword(s):  
Heat Transfer ◽  
Perturbation Method ◽  
Transfer Equation ◽  
Homotopy Perturbation Method ◽  
Heat Transfer Equation ◽  
Conduction Heat Transfer ◽  
Homotopy Perturbation ◽  
Runge Kutta Method ◽  
Engineering Problems ◽  
Specific Heat Coefficient

Analytical solutions play a very important role in heat transfer. In this paper, the He's homotopy perturbation method (HPM) has been applied to nonlinear convective-radiative non-Fourier conduction heat transfer equation with variable specific heat coefficient. The concept of the He's homotopy perturbation method are introduced briefly for applying this method for problem solving. The results of HPM as an analytical solution are then compared with those derived from the established numerical solution obtained by the fourth order Runge-Kutta method in order to verify the accuracy of the proposed method. The results reveal that the HPM is very effective and convenient in predicting the solution of such problems, and it is predicted that HPM can find a wide application in new engineering problems.

scholarly journals Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Daniel Olvera ◽  
Alex Elías-Zúñiga
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Response Curves ◽  
New Approach ◽  
Physical Systems ◽  
Homotopy Perturbation ◽  
Runge Kutta Method ◽  
Homotopy Analysis

We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM) that is based on the homotopy perturbation method (HPM) and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameterhby following the homotopy analysis method (HAM). At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.

scholarly journals The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System

2015 ◽  
Vol 2015 ◽  
pp. 1-17
Author(s):  
M. S. H. Chowdhury ◽  
Nur Isnida Razali ◽  
Waqar Asrar ◽  
M. M. Rahman
Keyword(s):  
Perturbation Method ◽  
Fourth Order ◽  
Homotopy Perturbation Method ◽  
Kutta Method ◽  
Time Intervals ◽  
Powerful Technique ◽  
Homotopy Perturbation ◽  
Runge Kutta Method ◽  
Hyperchaotic Lu System ◽  
Hyperchaotic Systems

The multistage homotopy-perturbation method (MHPM) is applied to the nonlinear chaotic and hyperchaotic Lü systems. MHPM is a technique adapted from the standard homotopy-perturbation method (HPM) where the HPM is treated as an algorithm in a sequence of time intervals. To ensure the precision of the technique applied in this work, the results are compared with a fourth-order Runge-Kutta method and the standard HPM. The results show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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