The homotopy analysis method for solving higher dimensional initial boundary value problems of variable coefficients

2009 ◽  
Vol 26 (5) ◽  
pp. 1021-1032 ◽  
Author(s):  
H. Jafari ◽  
M. Saeidy ◽  
M. A. Firoozjaee
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Analysis Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Variable Coefficients ◽  
Initial Boundary Value Problems ◽  
Analysis Method ◽  
Higher Dimensional ◽  
Homotopy Analysis ◽  
Initial Boundary Value

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 Homotopy Analysis Method for a Fractional Order Equation with Dirichlet and Non-Local Integral Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1167
Author(s):  
Said Mesloub ◽  
Saleem Obaidat
Keyword(s):  
Fractional Order ◽  
Homotopy Analysis Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Initial Boundary Value

The main purpose of this paper is to obtain some numerical results via the homotopy analysis method for an initial-boundary value problem for a fractional order diffusion equation with a non-local constraint of integral type. Some examples are provided to illustrate the efficiency of the homotopy analysis method (HAM) in solving non-local time-fractional order initial-boundary value problems. We also give some improvements for the proof of the existence and uniqueness of the solution in a fractional Sobolev space.

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.

Sign in / Sign up

Export Citation Format

Share Document