Related papers: About homotopy perturbation method for solving hea…
Homotopy perturbation method is used for solving the multi-point boundary value problems. The approximate solution is found in the form of a rapidly convergent series. Several numerical examples have been considered to illustrate the…
In this paper we discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators . We show that the main equations are inconsistent and for that reason the results may be of scarce utility.
We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exactly the same result by means of the Taylor series in the…
We show that a recent application of homotopy perturbation method to a class of ordinary differential equations yields either useless or wrong results.
In this study, a thorough investigation was conducted into the Homotopy Perturbation Method (HPM) and its application to solve the Burger and Blasius equations. The HPM is a mathematical technique that combines aspects of homotopy and…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian…
I discuss a recent application of homotopy perturbation and Adomian decomposition methods to the linear and nonlinear Schr\"odinger equations. I propose a generalization of the procedure for the treatment of a wider class of problems.
I discuss a recent application of homotopy perturbation method to a heat transfer problem. I show that the authors make infinity equal five and analyze the consequences of that magic.
In this work, Lienard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method. The amplitude and frequency obtained with this methodology are in good agreement with those calculated…
Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…
This paper deals the implementation of \emph{homotopy perturbation transform method} (HPTM) for numerical computation of initial valued autonomous system of time-fractional partial differential equations (TFPDEs) with proportional delay,…
We discuss a recent application of the Modified Homotopy Perturbation Method to the Fokker--Planck equation and show that the selected examples do not have any connection with actual physical problems.
In this paper we propose a reduction procedure for determining generalized travelling waves for first order quasilinear hyperbolic nonhomogeneous systems. The basic idea is to look for solutions of the governing model which satisfy a…
In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (with known solutions) to more complicated nonlinear…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of…
In this article, we apply Homotopy Perturbation Method (HPM) for solving three coupled non-linear equations which play an important role in biosystems. To illustrate the capability and reliability of this method. Numerical example is given…
The induction motor behaviour is represented by a fifth order differential equation model. Addition of a torque correction factor to the model accurately reproduces the transient torques and instantaneous real and reactive power flows of…
The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…