We describe a connection between discrete birth process and a certain family of multivariate interpolation polynomials. This enables us to compute all asymptotic moments of the birth process, generalizing previously known results for the mean and variance.

A multivariate kth divided diierence is proposed and shown to lead to new error formull for polynomial interpolation on some standard multivariate point sets. x1. Introduction In trying to understand what might be a reasonable way to describe the error in interpolation by polynomials on l R d , I came upon the following considerations: The standard error formula g(x) = g(a) + Z 1 0 D x?a g(a + ...

We present discretization schemes for the Poisson equation, the isothermal drift-diffusion equations, and a generalized higher-order moment equation of the Boltzmann transport equation for general orthogonal coordinate systems like cylindrical and spherical systems. The use of orthogonal coordinate systems allows to reduce the dimension of the problem from three to two. We give an approximation...