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 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.

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).

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 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 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 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.

scholarly journals Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Limei Yan
Keyword(s):  
Laplace Transform ◽  
Numerical Solutions ◽  
Convergent Series ◽  
Space Time ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Promising Tool ◽  
The Laplace Transform ◽  
Fokker Planck Equations ◽  
Fokker Planck

A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.

scholarly journals An Approximate Solution of Fractional Kolmogorov-Petrovskii-Piskunov Equations

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Sumaira Yousuf Khan ◽  
Sahaf Altaf Ahmed
Keyword(s):  
Homotopy Perturbation Method ◽  
Computational Cost ◽  
Classical Equation ◽  
Nonlinear Problems ◽  
Industrial Applications ◽  
Analytical Tool ◽  
Rapid Convergence ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Differential Transform

An approximate-analytical method known as Reduced Differential Transform Method (RDTM) is proposed to approximate the Fractional Kolmogorov- Petrovskii –Piskunov Equations. It is a powerful and convenient approximation analytical tool used for linear and nonlinear equations related to various science, engineering and industrial applications. Some illustrative examples are given to exemplify the competence of the proposed scheme and provide precise solutions for nonlinear problems. In addition, a comparison with the classical equation and Homotopy perturbation method illustrates the competency of the technique. The results show that the proposed technique requires minimum computational cost at rapid convergence. This method can be applied to other partial differential equations of fractional order for the analysis of their solutions.

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.

Sign in / Sign up

Export Citation Format

Share Document