scholarly journals Variational Homotopy Perturbation Method for Solving Higher Dimensional Initial Boundary Value Problems

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Perturbation Method ◽  
Boundary Value Problems ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Variable Coefficients ◽  
Initial Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Higher Dimensional ◽  
Initial Boundary Value

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM). We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.

scholarly journals Green’s function homotopy perturbation method for the initial-boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Wannika Sawangtong ◽  
Panumart Sawangtong
Keyword(s):  
Perturbation Method ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Initial Boundary Value

Abstract This article deals with the novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method, shortly called SGHPM. The SGHPM is a method which combines the homotopy perturbation method with Green’s function method. The convergence analysis for the SGHPM is shown. Furthermore, some examples are presented to illustrate the validity of the proposed method and to ensure that SGHPM is a technique which is powerful and efficient for finding approximate analytic solutions of IBVPs.

scholarly journals Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yanqin Liu
Keyword(s):  
Perturbation Method ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Initial Boundary Value

A variational homotopy perturbation method (VHPM) which is based on variational iteration method and homotopy perturbation method is applied to solve the approximate solution of the fractional initial boundary value problems. The nonlinear terms can be easily handled by the use of He's polynomials. It is observed that the variational iteration method is very efficient and easier to implements; illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

Initial-boundary value problems for linear PDEs with variable coefficients

2007 ◽  
Vol 143 (1) ◽  
pp. 221-242 ◽  
Author(s):  
P. A. TREHARNE ◽  
A. S. FOKAS
Keyword(s):  
Boundary Value Problems ◽  
Evolution Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Initial Boundary Value Problems ◽  
Linear Evolution ◽  
Higher Derivatives ◽  
Initial Boundary Value

AbstractA new approach for studying initial-boundary value problems for linear partial differential equations (PDEs) with variable coefficients was introduced recently by the second author, and was applied to PDEs involving second order derivatives. Here, we extend this approach further to solve an initial-boundary value problem for a third-order evolution PDE with a space-dependent coefficient. The analysis is presented in such a way that it can be applied to PDEs with higher derivatives, and thus provides a method for solving initial-boundary value problems for a certain class of linear evolution equations with variable coefficients of arbitrary order.

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