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.

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 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 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.

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 Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics Equation

2012 ◽  
Vol 8 (1) ◽  
pp. 55-61 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
Keyword(s):  
Laplace Transform ◽  
Gas Dynamics ◽  
Homotopy Perturbation Method ◽  
Nonlinear Problems ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform ◽  
Gas Dynamics Equation ◽  
Adomian’S Polynomials

Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics EquationIn this paper, we apply a combined form of the Laplace transform method with the homotopy perturbation method to obtain the solution of nonlinear gas dynamics equation. This method is called the homotopy perturbation transform method (HPTM). This technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that this scheme solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method. The results reveal that the homotopy perturbation transform method (HPTM) is very efficient, simple and can be applied to other nonlinear problems.

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 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.

Solution of Non-Linear RLC Circuit Equation Using the Homotopy Perturbation Transform Method

2021 ◽  
Vol 14 (1) ◽  
pp. 89-100
Keyword(s):  
Laplace Transform ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Rlc Circuit ◽  
Non Linear ◽  
The Laplace Transform

Abstract: In this paper, we apply the Homotopy Perturbation Transform Method (HPTM) to obtain the solution of Non-Linear RLC Circuit Equation. This method is a combination of the Laplace transform method with the homotopy perturbation method. The HPTM can provide analytical solutions to nonlinear equations just by employing the initial conditions and the nonlinear term decomposed by using the He’s polynomials. Keywords: Homotopy perturbation, Laplace transform, He’s polynomials, Non-linear RLC circuit equation.

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He’s Polynomial

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Dinkar Sharma ◽  
Prince Singh ◽  
Shubha Chauhan
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Present Scheme ◽  
Homotopy Perturbation ◽  
Kdv Equations ◽  
De Vries ◽  
The Laplace Transform ◽  
Fifth Order

AbstractIn this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He’s polynomials. Two test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM).

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