scholarly journals Recent Modification of Homotopy Perturbation Method for Solving System of Third Order PDEs

2020 ◽  
Vol 1530 ◽  
pp. 012073
Author(s):  
Luma Naji Mohammed Tawfiq ◽  
Huda Altaie
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Third Order ◽  
Homotopy Perturbation ◽  
Recent Modification

scholarly journals Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Zakeri ◽  
Azim Aminataei ◽  
Qodsiyeh Jannati
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Nonlinear Diffusion ◽  
Homotopy Perturbation Method ◽  
Finite Interval ◽  
Nonlinear Diffusion Equation ◽  
Third Order ◽  
Homotopy Perturbation ◽  
Ill Posed

We consider a Cauchy problem of unidimensional nonlinear diffusion equation on finite interval. This problem is ill-posed and its approximate solution is unstable. We apply the He's homotopy perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductivity term in diffusion equation has a specified condition, the above solution can be estimated. Finally, a numerical experiment is provided to illustrate the method.

scholarly journals Uncharted Stable Peninsula for Multivariable Milling Tools by High-Order Homotopy Perturbation Method

2020 ◽  
Vol 10 (21) ◽  
pp. 7869 ◽  
Author(s):  
Jose de la Luz Sosa ◽  
Daniel Olvera-Trejo ◽  
Gorka Urbikain ◽  
Oscar Martinez-Romero ◽  
Alex Elías-Zúñiga ◽  
...  
Keyword(s):  
Differential Equation ◽  
Perturbation Method ◽  
Delay Differential Equation ◽  
Homotopy Perturbation Method ◽  
Multiple Delays ◽  
Third Order ◽  
Method Performance ◽  
Homotopy Perturbation ◽  
The Stability ◽  
Delay Differential

In this work, a new method for solving a delay differential equation (DDE) with multiple delays is presented by using second- and third-order polynomials to approximate the delayed terms using the enhanced homotopy perturbation method (EMHPM). To study the proposed method performance in terms of convergency and computational cost in comparison with the first-order EMHPM, semi-discretization and full-discretization methods, a delay differential equation that model the cutting milling operation process was used. To further assess the accuracy of the proposed method, a milling process with a multivariable cutter is examined in order to find the stability boundaries. Then, theoretical predictions are computed from the corresponding DDE finding uncharted stable zones at high axial depths of cut. Time-domain simulations based on continuous wavelet transform (CWT) scalograms, power spectral density (PSD) charts and Poincaré maps (PM) were employed to validate the stability lobes found by using the third-order EMHPM for the multivariable tool.

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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