scholarly journals Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yanqin Liu
Keyword(s):  
Approximate Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Transformation Method ◽  
High Accuracy ◽  
Homotopy Perturbation ◽  
He’S Polynomials

A homotopy perturbation transformation method (HPTM) which is based on homotopy perturbation method and Laplace transform is first applied to solve the approximate solution of the fractional nonlinear equations. The nonlinear terms can be easily handled by the use of He's polynomials. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

An easy and computable approximation for Troesch’s problem by using the Laplace Transform-Homotopy Perturbation Method

2019 ◽  
Vol 29 ◽  
pp. 1-14
Author(s):  
U. Filobello-Nino ◽  
H. Vazquez-Leal ◽  
A. L. Herrera-May ◽  
V. M. Jimenez-Fernandez ◽  
J. Cervantes-Perez ◽  
...  
Keyword(s):  
Approximate Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Absolute Relative Error ◽  
Homotopy Perturbation ◽  
Average Absolute Relative Error ◽  
The Laplace Transform ◽  
Troesch’S Problem

This work introduces the Laplace Transform-Homotopy Perturbation Method (LT-HPM) in order to provide an approximate solution for Troesch’s problem. After comparing figures between exact and approximate solutions, as well as the average absolute relative error (AARE) of the approximate solutions of this research, with others reported in the literature, it can be said that the proposed solutions are accurate and handy. In conclusion, LT-HPM is a potentially useful tool.

scholarly journals Second Approximate Solution of Duffing Equation with Strong Nonlinearity by Homotopy Perturbation Method

1970 ◽  
Vol 30 ◽  
pp. 59-75
Author(s):  
M Alhaz Uddin ◽  
M Abdus Sattar
Keyword(s):  
Approximate Solution ◽  
Nonlinear Systems ◽  
Perturbation Method ◽  
Differential System ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Second Order ◽  
Strong Nonlinearity ◽  
Analytical Technique ◽  
Homotopy Perturbation

 In this paper, the second order approximate solution of a general second order nonlinear ordinary differential system, modeling damped oscillatory process is considered. The new analytical technique based on the work of He’s homotopy perturbation method is developed to find the periodic solution of a second order ordinary nonlinear differential system with damping effects. Usually the second or higher order approximate solutions are able to give better results than the first order approximate solutions. The results show that the analytical approximate solutions obtained by homotopy perturbation method are uniformly valid on the whole solutions domain and they are suitable not only for strongly nonlinear systems, but also for weakly nonlinear systems. Another advantage of this new analytical technique is that it also works for strongly damped, weakly damped and undamped systems. Figures are provided to show the comparison between the analytical and the numerical solutions. Keywords: Homotopy perturbation method; damped oscillation; nonlinear equation; strong nonlinearity. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 59-75  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8504

scholarly journals AN ACCURATE SOLUTION TO THE LOTKA-VOLTERRA EQUATIONS BY MODIFIED HOMOTOPY PERTURBATION METHOD

2012 ◽  
Vol 09 ◽  
pp. 326-333 ◽  
Author(s):  
M. S. H. CHOWDHURY ◽  
M. M. RAHMAN
Keyword(s):  
Perturbation Method ◽  
Numerical Solution ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Volterra Equations ◽  
Algebraic Equations ◽  
Time Intervals ◽  
Homotopy Perturbation

In this paper, we suggest a method to solve the multispecies Lotka-Voltera equations. The suggested method, which we call modified homotopy perturbation method, can be considered as an extension of the homotopy perturbation method (HPM) which is very efficient in solving a varety of differential and algebraic equations. The HPM is modified in order to obtain the approximate solutions of Lotka-Voltera equation response in a sequence of time intervals. In particular, the example of two species is considered. The accuracy of this method is examined by comparison with the numerical solution of the Runge-Kutta-Verner method. The results prove that the modified HPM is a powerful tool for the solution of nonlinear equations.

scholarly journals A handy approximate solution for a squeezing flow between two infinite plates by using of Laplace transform-homotopy perturbation method

SpringerPlus ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 421 ◽  
Author(s):  
Uriel Filobello-Nino ◽  
Hector Vazquez-Leal ◽  
Juan Cervantes-Perez ◽  
Brahim Benhammouda ◽  
Agustin Perez-Sesma ◽  
...  
Keyword(s):  
Approximate Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Squeezing Flow ◽  
Homotopy Perturbation

scholarly journals Variational Approximate Solutions of Fractional Nonlinear Nonhomogeneous Equations with Laplace Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yanqin Liu ◽  
Fengsheng Xu ◽  
Xiuling Yin
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
The Laplace Transform

A novel modification of the variational iteration method is proposed by means of Laplace transform and homotopy perturbation method. The fractional lagrange multiplier is accurately determined by the Laplace transform and the nonlinear one can be easily handled by the use of He’s polynomials. Several fractional nonlinear nonhomogeneous equations are analytically solved as examples and the methodology is demonstrated.

scholarly journals Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
U. Filobello-Nino ◽  
H. Vazquez-Leal ◽  
A. Sarmiento-Reyes ◽  
B. Benhammouda ◽  
V. M. Jimenez-Fernandez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Perturbation Method ◽  
Nonlinear Differential Equation ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Partial Slip ◽  
Homotopy Perturbation

The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient.

scholarly journals Numerical inverse Laplace homotopy technique for fractional heat equations

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 185-194 ◽  
Author(s):  
Mehmet Yavuz ◽  
Necati Ozdemir
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Heat Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Proposed Model ◽  
Fractional Pde ◽  
The Laplace Transform

In this paper, we have aimed the numerical inverse Laplace homotopy technique for solving some interesting 1-D time-fractional heat equations. This method is based on the Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method. Firstly, we have applied to the fractional 1-D PDE by using He?s polynomials. Then we have used Laplace transform method and discussed how to solve these PDE by using Laplace homotopy perturbation method. We have declared that the proposed model is very efficient and powerful technique in finding approximate solutions to the fractional PDE.

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.

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

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