The probability density function (PDF) of a random variable associated with the solution partial differential equation (PDE) parameters is approximated using truncated series expansion. PDE solved two stochastic finite element methods, Monte Carlo sampling and Galerkin method global polynomials. functional PDE, such as average over physical domain. are obtained considering number terms in Gram-...

The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a three-term recurrence relation for these dual polynomials are explicitly obtained. The completeness property of dual alternative q-Charlier polynomials is also esta...

Idealizing matter as a pressureless fluid and representing its motion by a peculiar-velocity field superimposed on a homogeneous and isotropic Hubble expansion, we apply (Lagrangian) spatial averaging on an arbitrary domain D to the (nonlinear) equations of Newtonian cosmology and derive an exact, general equation for the evolution of the (domain dependent) scale factor aD (t). We consider the ...

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distribu...

In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be closed. Using new weighted discrete So...

A systolic algorithm is devised for solving a class of Riccati and Lyapunov equations, which makes use of a factored version of the matrix sign recursions due to Charlier & Van Dooren 1]. The original algorithm is worked into an alternative Jacobi-type algorithm, which is readily implemented on a systolic array. Compared to the array of Charlier & Van Dooren, the present algorithm/array is conc...

In this paper, we develop a new approximation for nonstationary multiserver queues with abandonment. Our method uses the Poisson–Charlier polynomials, which are a discrete orthogonal polynomial sequence that is orthogonal with respect to the Poisson distribution. We show that by appealing to the Poisson–Charlier polynomials that we can estimate the mean, variance, and probability of delay of ou...