Homotopy perturbation technique

1999 ◽  
Vol 178 (3-4) ◽  
pp. 257-262 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Perturbation Technique ◽  
Homotopy Perturbation ◽  
Homotopy Perturbation Technique

scholarly journals Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jing Wang ◽  
Bo Han
Keyword(s):  
Image Reconstruction ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Perturbation Technique ◽  
Inversion Method ◽  
Impedance Tomography ◽  
Data Noise ◽  
Homotopy Perturbation ◽  
Ill Posed ◽  
Homotopy Perturbation Technique

The image reconstruction for electrical impedance tomography (EIT) mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.

scholarly journals Numerical Approximate Solution to Flow over a Flat Plate ( the Balusis Problem) By Perturbation Iteration- Algorithm

2021 ◽  
Author(s):  
Abeer Jasim
Keyword(s):  
Continuity Equation ◽  
Perturbation Technique ◽  
Navier Stokes ◽  
Iteration Algorithm ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Homotopy Perturbation ◽  
Blasius Problem ◽  
Layer Flow ◽  
Homotopy Perturbation Technique

This paper applied perturbation iteration- algorithm (PI-A) to solve the problem of the incompressible two-dimensional laminar boundary layer flow over a flat plat as wall as called the Blasius problem (BP). BP is governed by Navier- Stokes equation (NSE) and continuity equation which were transformed into ordinary differential equation using similarity transforms. The results presented are tabulated for similarity stream function and can be seen highly of accuracy through comparable with that obtained by Ganji et al.[3] who studied BP using Homotopy perturbation technique (HPT) , Research results for the same problem using the variationally This paper applied perturbation iteration- algorithm (PI-A) to solve the problem of the incompressible two-dimensional laminar boundary layer flow over a flat plat as wall as called the Blasius problem (BP). BP is governed by Navier- Stokes equation (NSE) and continuity equation which were transformed into ordinary differential equation using similarity transforms. The results presented are tabulated for similarity stream function and can be seen highly of accuracy through comparable with that obtained by Ganja et al.[3] who studied BP using Homotopy perturbation technique (HPT) , Research results for the same problem using the variational iteration technique (VIT) before Aiyesimi and Niyi[5] and results numerical by Blasius[1]. Finally, The method that is efficient and widely applicable for solving ODE.

scholarly journals Modified Homotopy Perturbation Technique for the Approximate Solution of Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Farooq Ahmed Shah
Keyword(s):  
Approximate Solution ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Perturbation Technique ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
New Methods ◽  
And Performance ◽  
Homotopy Perturbation Technique

We use a new modified homotopy perturbation method to suggest and analyze some new iterative methods for solving nonlinear equations. This new modification of the homotopy method is quite flexible. Various numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations.

scholarly journals An Analytical View of Fractional-Order Fisher’s Type Equations within Caputo Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Nehad Ali Shah
Keyword(s):  
Applied Sciences ◽  
Fractional Order ◽  
Perturbation Technique ◽  
Analytical Investigation ◽  
Homotopy Perturbation ◽  
Research Article ◽  
The Given ◽  
Homotopy Perturbation Technique

The present research article is related to the analytical investigation of some nonlinear fractional-order Fisher’s equations. The homotopy perturbation technique and Shehu transformation are implemented to discuss the fractional view analysis of Fisher’s equations. For a better understanding of the proposed procedure, some examples related to Fisher’s equations are presented. The identical behavior of the derived and actual solutions is observed. The solutions at different fractional are calculated, which describe some useful dynamics of the given problems. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences.

scholarly journals Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Kamsing Nonlaopon ◽  
Muhammad Naeem ◽  
Ahmed M. Zidan ◽  
Rasool Shah ◽  
Ahmed Alsanad ◽  
...  
Keyword(s):  
Fractional Order ◽  
Real World ◽  
Analytical Method ◽  
Laplace Transformation ◽  
Fractional Derivatives ◽  
Perturbation Technique ◽  
Homotopy Perturbation ◽  
Real World Problem ◽  
Kernel Operators ◽  
Homotopy Perturbation Technique

This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives.

Modal Modification of Damped Asymmetric Systems without Using the Left Eigenvectors

2014 ◽  
Vol 490-491 ◽  
pp. 331-335 ◽  
Author(s):  
Li Li ◽  
Yu Jin Hu ◽  
Xue Lin Wang
Keyword(s):  
Dynamic System ◽  
Perturbation Technique ◽  
Projection Technique ◽  
Reduced Basis ◽  
Homotopy Perturbation ◽  
Modal Truncation ◽  
Rotor Dynamic ◽  
Homotopy Perturbation Technique

This study focuses on the prediction of complex eigenpairs of modified asymmetric systems. A method, which combines the reduced basis and the projection technique, is presented to predict the eigenpairs of modified asymmetric systems. The reduced basis obtained using the homotopy perturbation technique only requires the eigensolution of interest such that the modal truncation problem can be avoided. More importantly, the method can be carried out without using the left eigenvectors. The accuracy of the reduced basis approximation can be improved by introducing the projection technique. A rotor dynamic system is used to illustrate the capacity of predicting the changes of eigensolutions.

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