The present paper deals with the homotopy perturbation method. The question of whether the homotopy perturbation method is simply the conventional Taylor series expansion is examined. It is proven that under particular choices of the auxiliary parameters the homotopy perturbation method is indeed the Taylor series expansion of the sought solution of nonlinear equations.

A reorganized perturbation expansion with a propagator of soft infrared behavior is used to study the critical behavior of the mass gap. The condition of relativistic covariance fixes the form of the soft propagator. Finite approximants to the correlation critical exponent can be obtained in every order of the modified, soft perturbation expansion. Alternatively, a convergent series of exponent...

In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a rst-order perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variation in the perturbed quantity. Up to the higher-order terms that are ignored in the expansion, these st...

The derivation of effective spin models describing the low energy magnetic properties of undoped CuO 2 –planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi–band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La 2 CuO 4. Starting from a con...

motivating the perturbations of frames in hilbert and banach spaces, in this paper we introduce the invariance of fr'echet frames under perturbation. also we show that for any fr'echet spaces, there is a fr'echet frame and any element in these spaces  has a series expansion.

We apply the δ-expansion perturbation scheme to the λφ4 self-interacting scalar field theory in 3+1 D at finite temperature. In the δ-expansion the interaction term is written as λ(φ2)1+δ and δ is considered as the perturbation parameter. We compute, in this perturbation approach, the renormalized mass at finite temperature from which we get the critical temperature. The results are compared wi...

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the...