scholarly journals APPLICATION OF LAPLACE TRANSFORM HOMOTOPY PERTURBATION METHOD TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

2016 ◽  
Vol 05 (05) ◽  
pp. 404-408
Author(s):  
Prem Kiran G. Bhadane .
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

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 Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Convergence Analysis ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.

scholarly journals He-Laplace Method for Linear and Nonlinear Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hradyesh Kumar Mishra ◽  
Atulya K. Nagar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Laplace Method ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
New Treatment

A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.

scholarly journals Analytical Study of Some Important Generalized Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Marwan Alquran ◽  
Mahmoud Mohammad ◽  
Ahmad Ababneh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Analytical Study ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Fisher Equation ◽  
Convection Term ◽  
Partial Differential ◽  
Homotopy Perturbation

The aim of this paper is to extend the use of homotopy perturbation method (HPM) to study the solutions for some important generalized nonlinear partial differential equations (PDEs) such as Fisher equation with convection term, Sharma-Tasso-Olver (STO) equation, and Fitzhugh-Nagumo (FN) equation.

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