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.

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.

Homotopy Perturbation Transform Method with He’s Polynomial for Solution of Coupled Nonlinear Partial Differential Equations

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Dinkar Sharma ◽  
Prince Singh ◽  
Shubha Chauhan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Two Dimensions ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform

AbstractIn this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers’ equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He’s polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.

scholarly journals Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Accelerated Convergence ◽  
Homotopy Perturbation ◽  
Long Wave ◽  
Approximate Analytical Solutions ◽  
Regularized Long Wave Equation ◽  
Regular Homotopy

The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.

Nonlinear Flutter of Laminated Composite Plates Resting on Nonlinear Elastic Foundations Using Homotopy Perturbation Method

2015 ◽  
Vol 15 (05) ◽  
pp. 1450072 ◽  
Author(s):  
Ali A. Yazdi
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Composite Plates ◽  
Laminated Plates ◽  
Geometrically Nonlinear ◽  
Aerodynamic Pressure ◽  
Nonlinear Flutter ◽  
Homotopy Perturbation ◽  
Nonlinear Elastic

In this paper, the applicability of the homotopy perturbation method (HPM) in analyzing the flutter of geometrically nonlinear cross-ply rectangular laminated plates resting on nonlinear elastic foundation is investigated. The piston theory is employed to evaluate the aerodynamic pressure acting on the plate. The von Karman geometric nonlinear theory is used to construct the governing equations of the system. The Galerkin's method is used to reduce the nonlinear partial differential equations to a nonlinear second-order ordinary differential equation, and the HPM is employed to study the effect of initial deflection, aspect ratio and stacking sequence on the flutter pressure of cross-ply laminated plates. The results show that the first approximation of the HPM leads to highly accurate solutions for the geometrically nonlinear flutter of cross-ply rectangular laminated plates subjected to the aerodynamic pressure.

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