Comparison between variational iteration method and homotopy perturbation method for linear and nonlinear partial differential equations with the nonhomogeneous initial conditions

2009 ◽  
Vol 26 (6) ◽  
pp. 1581-1593
Author(s):  
İnan Ateş ◽  
Ahmet Yıldırım
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Variational Iteration Method ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

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.

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.

Application of New Homotopy Perturbation Method for Solving Partial Differential Equations

2018 ◽  
Vol 15 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Musa R. Gad-Allah ◽  
Tarig M. Elzaki
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Novel Technique ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear Differential

In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

scholarly journals On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
E. E. Eladdad ◽  
E. A. Tarif
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In the current work, a combination between a new integral transform and the homotopy perturbation method is presented. This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations.

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