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).

A reliable algorithm for KdV equations arising in warm plasma

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Amit Goswami ◽  
Jagdev Singh ◽  
Devendra Kumar
Keyword(s):  
Homotopy Perturbation Method ◽  
Nonlinear Problems ◽  
Convergent Series ◽  
Science And Engineering ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Kdv Equations ◽  
The Laplace Transform ◽  
Warm Plasma

AbstractThe aim of the present work is to propose a simple and reliable algorithm namely homotopy perturbation transform method (HPTM) for KdV equations in warm plasma. The homotopy perturbation transform method is a combined form of the Laplace transform method with the homotopy perturbation method. In this method, the solution is calculated in the form of a convergent series with an easily computable compact. To illustrate the simplicity and reliability of the method, several examples are provided. In this paper, the homotopy perturbation transform method has been applied to obtain the solution of the KdV, mKdV, K(2, 2) and K(3,3) equations. We compared our solutions with the exact solutions. Results illustrate the applicability, efficiency and accuracy of HPTM to solve nonlinear equations despite needlessness to any linearization or perturbation. It is predicted that the proposed algorithm can be widely applied to other nonlinear problems in science and engineering.

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 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 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.

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.

scholarly journals Analytical and Approximate Solution for Solving the Vibration String Equation with a Fractional Derivative

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1154
Author(s):  
Temirkhan S. Aleroev ◽  
Asmaa M. Elsayed
Keyword(s):  
Fractional Derivative ◽  
Homotopy Perturbation Method ◽  
Analytic Solution ◽  
Separation Of Variables ◽  
Fourier Method ◽  
String Equation ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform

This paper is proposed for solving a partial differential equation of second order with a fractional derivative with respect to time (the vibration string equation), where the fractional derivative order is in the range from zero to two. We propose a numerical solution that is based on the Laplace transform method with the homotopy perturbation method. The method of the separation of variables (the Fourier method) is constructed for the analytic solution. The derived solutions are represented by Mittag–LefLeffler type functions. Orthogonality and convergence of the solution are discussed. Finally, we present an example to illustrate the methods.

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 An efficient approach for solution of fractional-order Helmholtz equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nehad Ali Shah ◽  
Essam R. El-Zahar ◽  
Mona D. Aljoufi ◽  
Jae Dong Chung
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Hybrid Technique ◽  
Science And Engineering ◽  
Helmholtz Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Suggested Technique ◽  
Present Technique

AbstractIn this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform method and the homotopy perturbation method are amalgamated. Three problems are solved to validate and demonstrate the efficacy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the results by other techniques. It is shown that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

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