Laplace Decomposition Algorithm and Pade Approximants for Population Model

Two-point Pade approximants

We present analytic estimates for the energy levels of N electrons (N = 2−5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter β=(effective Rydberg/effective dot energy)1/6. Two-point Pade approximants are obtained from the series expansions of the energy ...

Pade Approximants and Borel Summation for QCD Perturbation Expansions

We study the applicability of Pade Approximants (PA) to estimate a ”sum” of asymptotic series of the type appearing in QCD. We indicate that one should not expect PA to converge for positive values of the coupling constant and propose to use PA for the Borel transform of the series. If the latter has poles on the positive semiaxis, the Borel integral does not exist, but we point out that the Ca...

The Berlekamp-Massey Algorithm. A Sight from Theory of Pade Approximants and Orthogonal Polynomials

In this paper we interpret the Berlekamp-Massey algorithm (BMA) for synthesis of linear feedback shift register (LFSR) as an algorithm computing Pade approximants for Laurent series over arbitrary field. This interpretation of the BMA is based on a iterated procedure for computing of the sequence of polynomials orthogonal to some sequence of polynomial spaces with scalar product depending on th...

Compare Adomian Decomposition Method and Laplace Decomposition Method for Burger's-Huxley and Burger's-Fisher equations

In this paper, Adomian decomposition method (ADM) and Laplace decomposition method (LDM) used to obtain series solutions of Burgers-Huxley and Burgers-Fisher Equations. In ADM the algorithm is illustrated by studying an initial value problem and LDM is based on the application of Laplace transform to nonlinear partial differential equations. In ADM only few terms of the expansion are required t...

On the Laplace transform decomposition algorithm for solving nonlinear differential equations