In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of  integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention  results on the weighted modulus of continuity for the genuine operators.

We study traveling wave solutions for the class of scalar reaction-diffusion equations ∂u ∂t = ∂u ∂x + fm(u), where the family of potential functions {fm} is given by fm(u) = 2u (1 − u). For each m ≥ 1 real, there is a critical wave speed ccrit(m) that separates waves of exponential structure from those which decay only algebraically. We derive a rigorous asymptotic expansion for ccrit(m) in th...

Effective boundary conditions (wall laws) are commonly employed to approximate PDEs in domains with rough boundaries, but it is neither easy to design such laws nor to estimate the related approximation error. A two-scale asymptotic expansion based on a domain decomposition result is used here to mitigate such difficulties, and as an application we consider the Poisson equation. The proposed sc...

The asymptotic expansion technique is used to obtain the two-dimensional dynamic equations of thin micropolar elastic plates from the three-dimensional dynamic equations of micropolar elasticity theory. To this end, all the ®eld variables are scaled via an appropriate thickness parameter such that it re ̄ects the expected behavior of the plate. A formal power series expansion of the three-dimens...

In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such an expansion is applied to improve the accuracy of the eigenvalue approximations. Furthermore, we also prove the superclose property between the finite elemen...

In this paper, a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established. Abstract lemmas for the error of the eigenvalue approximations are obtained. Based on the asymptotic error expansion formulas, the Richardson extrapolation method is employed to improve the accuracy of the approximations for ...

We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z , where z is a complex variable satisfying 0 arg z 2 π . A summary of the asymptotic properties of Gn(ix) for real values of x and an approximation for its extreme zeros as n→∞ are given. When the variables are such that z/n is finite, an expansion is obtained using the method of steepest descents ...

This paper presents a nonstandard local approach to Richardson extrapolation, when it is used to increase the accuracy of the standard finite element approximation of solutions of second order elliptic boundary value problems in RN , N ≥ 2. The main feature of the approach is that it does not rely on a traditional asymptotic error expansion, but rather depends on a more easily proved weaker a p...