Determination of Critical Buckling Loads for Euler Columns of Variable Flexural Stiffness with a Continuous Elastic Restraint Using Homotopy Perturbation Method

2009 ◽  
Vol 10 (2) ◽  
Author(s):  
S. B. Coşkun
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Flexural Stiffness ◽  
Buckling Loads ◽  
Homotopy Perturbation

scholarly journals ANALYSIS OF TILT‐BUCKLING OF EULER COLUMNS WITH VARYING FLEXURAL STIFFNESS USING HOMOTOPY PERTURBATION METHOD

2010 ◽  
Vol 15 (3) ◽  
pp. 275-286 ◽  
Author(s):  
Safa Bozkurt Coşkun
Keyword(s):  
Stability Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Elastic Stability ◽  
Efficient Technique ◽  
Mode Shapes ◽  
Flexural Stiffness ◽  
Buckling Loads ◽  
Homotopy Perturbation ◽  
Different Types

In this paper, the Homotopy Perturbation Method (HPM), is introduced for elastic stability analysis of tilt‐buckled columns with variable flexural stiffness. Buckling loads and corresponding mode shapes are determined considering different types of variations in flexural stiffness of columns. The proposed approach is an efficient technique for the elastic stability analysis of specified problems.

Homotopy Perturbation Method for General Form of Porous Medium Equation

2009 ◽  
Vol 12 (11) ◽  
pp. 1121-1127 ◽  
Author(s):  
Jafar Biazar ◽  
Zainab Ayati ◽  
Hamideh Ebrahimi
Keyword(s):  
Porous Medium ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Porous Medium Equation ◽  
Homotopy Perturbation ◽  
Medium Equation

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.

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