scholarly journals Homotopy Perturbation Transform Method for Extensible Beam Equations

2019 ◽  
Vol 8 (1) ◽  
pp. 15-20
Author(s):  
Khaled A. Ishag ◽  
Faris Azhari Okasha
Keyword(s):  
Nonlinear Equation ◽  
Analytical Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fixed Distance ◽  
Beam Equations ◽  
Initial Boundary Value ◽  
Transverse Deflection

In this paper, we apply analytical method (homotopy perturbation transformmethod), for solving extensible beam, we discuss certain initial- boundary value problems for the nonlinear equation. This equation wasproposed by Woiniwsky- Krieger as a model for transverse deflection of an extensible beam of natural length whose ends are held a fixed distance apart.

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.

scholarly journals Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

2011 ◽  
Vol 152 (3) ◽  
pp. 473-496 ◽  
Author(s):  
DAVID A. SMITH
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Evolution Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Transform Method ◽  
Arbitrary Boundary ◽  
Initial Boundary Value ◽  
Well Posed

AbstractWe study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series.The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

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 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.

The Analytical Method in Geomechanics

2007 ◽  
Vol 60 (3) ◽  
pp. 87-106 ◽  
Author(s):  
A. P. S. Selvadurai
Keyword(s):  
Porous Media ◽  
Boundary Value Problems ◽  
Analytical Method ◽  
Boundary Value ◽  
Practical Importance ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Flow And Transport ◽  
Initial Boundary Value

This article presents an overview of the application of analytical methods in the theories of elasticity, poroelasticity, flow, and transport in porous media and plasticity to the solution of boundary value problems and initial boundary value problems of interest to geomechanics. The paper demonstrates the role of the analytical method in geomechanics in providing useful results that have practical importance, pedagogic value, and serve as benchmarking tools for calibrating computational methodologies that are ultimately used for solving more complex practical problems in geomechanics. There are 315 references cited in this article.

scholarly journals Unified Transform method for the Schr¨odinger Equation on a Simple Metric Graph

2019 ◽  
pp. 412-420
Author(s):  
Gulmirza Khudayberganov ◽  
Zarifboy A. Sobirov ◽  
Mardonbek R. Eshimbetov
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Metric Graphs ◽  
Transform Method ◽  
Star Graphs ◽  
Representation Of Solutions ◽  
Branching Point ◽  
Fokas Method ◽  
The Fourier Transform ◽  
Initial Boundary Value

Integral-representation of solutions of the initial-boundary value problems for the Schr¨odinger equation on simple metric graphs was obtained with the use of the Fokas method. This method uses special gen- eralization of the Fourier transform that is referred to as the unified transform. Obtained representation of solutions of the problem for open and closed simple star graphs allows one to identify transmitted, reflected and trapped waves at the graph branching point

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