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 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 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.

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 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

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

2021 ◽  
Author(s):  
Rachid Belgacem ◽  
Ahmed Bokhari ◽  
Salih Djilali ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Operational Matrix ◽  
Inversion Method ◽  
Numerical Inversion ◽  
Homotopy Perturbation ◽  
Boubaker Polynomials ◽  
The Laplace Transform ◽  
Good Agreement

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

scholarly journals Modified homotopy perturbation method coupled with Laplace transform for fractional heat transfer and porous media equations

2013 ◽  
Vol 17 (5) ◽  
pp. 1409-1414 ◽  
Author(s):  
Li-Mei Yan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform ◽  
Porous Media Equations ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

The purpose of this paper is to extend the homotopy perturbation method to fractional heat transfer and porous media equations with the help of the Laplace transform. The fractional derivatives described in this paper are in the Caputo sense. The algorithm is demonstrated to be direct and straightforward, and can be used for many other non-linear fractional differential 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 A New Efficient Method for Solving Two-Dimensional Burgers' Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Hossein Aminikhah
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Efficient Method ◽  
Homotopy Perturbation Method ◽  
Burgers Equation ◽  
Two Dimensional ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform

We introduce a new hybrid of the Laplace transform method and new homotopy perturbation method (LTNHPM) that efficiently solves nonlinear two-dimensional Burgers’ equation. Three examples are given to demonstrate the efficiency of the new method.

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 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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