where ∇ and ∇· are the gradient and divergence operators, Ω ⊂ R is an open bounded cubic domain with boundary Γ, n indicates the outward unit normal vector along Γ, A−1 = (αij)3×3 is a full positive definite matrix uniformly in Ω. Mixed finite element methods [1] should be employed to discretize the system (1.1). The main content of this paper is to present an analysis for the extrapolation of ...

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

For an ATM multiplexer we develop a recursive asymptotic expansion method for approximating the queue length distribution and investigate the radius of convergence of the queue asymptotic expansion series. The analysis focuses on “small” to “moderate” buffer sizes under the conditions of strictly stable multiple time scale arrivals. For a class of examples we analytically determine the radius o...

Recently Box and McKellar and Fymat have presented analytic inversion formulae for multispectral extinction data in the anomalous diffraction approximation. In this paper, we shall examine the relationship between these two formulae, and in the process we shall derive both the power series expansion and the asymptotic expansion for the extinction in this approximation.

In the paper, we discuss the transformation of the asymptotic expansion for the distribution of a statistic admitting Edgeworth expansion if the sample size is replaced by a random variable.We demonstrate that all those statistics that are regarded as asymptotically normal in the classical sense, become asymptotically Laplace or Student if the sample size is random. Thus, the Laplace and Studen...

We developed a new scheme for computing ”Greeks” of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asympt...

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff functions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean re...

the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...