scholarly journals Homotopy perturbation method with an auxiliary term for the optimal design of a tangent nonlinear packaging system

2019 ◽  
Vol 38 (3-4) ◽  
pp. 1075-1080 ◽  
Author(s):  
Wenxuan Kuang ◽  
Jun Wang ◽  
Chongxing Huang ◽  
Lixin Lu ◽  
De Gao ◽  
...  
Keyword(s):  
Optimal Design ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Packaging System ◽  
Homotopy Perturbation

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 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%.

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. 

A new modification of the homotopy perturbation method

2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi
Keyword(s):  
Comparative Analysis ◽  
Error Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillators ◽  
Absolute Error ◽  
New Method ◽  
Optimal Analysis ◽  
Homotopy Perturbation ◽  
Accuracy And Precision

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

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