In this paper we prove a conjecture on a common region of a convergence of Padé iterations for the matrix sector function. For this purpose we show that all Padé approximants to a special case of hypergeometric function have a power series expansion with positive coefficients. Using a sharpened version of Schwarz’s lemma, we also demonstrate a better estimate of the convergence speed. Our resul...

In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from DTM  and  predi...

In this paper, the differential transformation method (DTM) was applied to solve fuzzy fractional heat equations. The elementary properties of this method were given. The approximate and exact solutions of these equations were calculated in the form of series with easily computable terms. The proposed method was also illustrated by some examples. The results revealed that DTM is a highly effect...

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

We rederive AdS/CFT predictions for infrared two-point functions by an entirely four dimensional approach, without reference to holography. This approach, originally due to Migdal in the context of QCD, utilizes an extrapolation from the ultraviolet to the infrared using a Padé approximation of the two-point function. We show that the Padé approximation and AdS/CFT give the same leading order p...

In this paper, we introduce a modification of the Picard iteration method (PIM) using Padé approximation and so called Picard-Padé technique. Special attention is given to study the convergence analysis of the proposed method. Convergence analysis is reliable enough to estimate the maximum absolute error of the solution given by PIM. A basic enzyme kinetics is used to test the effectiveness of ...

in this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (dtm). this is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. several numerical examples are given and by comparing the numerical results obtained from dtm  and  predi...

in this paper, free vibration of an Euler-Bernoulli beam with variable cross-section resting on elastic foundation and under axial tensile force is considered. Beam’s constant height and exponentially varying width yields variable cross-section. The problem is handled for three different boundary conditions: clamped-clamped, simply supported-simply supported and clamp-free beams. First, the equ...

In this work, a solution strategy based on the use of Padé approximants is investigated for efficient solution of parametric finite element problems such as, for example, frequency sweep analyses. An improvement to the Padé-based expansion of the solution vector components is proposed, suggesting the advantageous a priori estimate of the poles of the solution. This allows for the intervals of a...

Convergence of diagonal Padé approximants is studied for a class of functions which admit the integral representation F(λ) = r1(λ) R 1 −1 tdσ(t) t−λ + r2(λ), where σ is a finite nonnegative measure on [−1, 1], r1, r2 are real rational functions bounded at ∞, and r1 is nonnegative for real λ. Sufficient conditions for the convergence of a subsequence of diagonal Padé approximants of F on R \ [−1...