Abstract In this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for third derivatives in truncation error remainder, two high-order compact LOD schemes are established solving two- three- dimensional advection equations, respectively. They have fourth-order accuracy both time space. By von Neumann analysis it shows that unconditionally stable. Bes...

In the past decade a lot of work has been done on the subject of multivariate Pad6 approximation theory and so it would be interesting to compare some different definitions. Let us first take a look at the univariate case. It is well known that univariate Pad6 approximants can be obtained in several equivalent ways and that they satisfy some typical properties. We will briefly repeat the defini...

Abstract In this paper, we give the series expansion for the stationary probabilities πn of the queue length of an M/D/1 queue based on analytic properties of the probability generating function π(z). We determine the poles and their associated residues of π(z), then give the partial fraction expansion of π(z). The series expansion of πn are given by the poles and residues. We also give an uppe...

With the help of a simple variational procedure it is possible to convert the partial sums of order N of many divergent series expansions f(g) = ∑∞ n=0 ang n into partial sums ∑N n=0 bng −ωn, where 0 < ω < 1 is a parameter that parametrizes the approach to the large-g limit. The latter are partial sums of a strong-coupling expansion of f(g) which converge against f(g) for g outside a certain di...

We develop a simple and e cient algorithm to compute Riemann-Roch spaces of divisors in general algebraic function elds which does not use the Brill-Noether method of adjoints nor any series expansions. The basic idea also leads to an elementary proof of the Riemann-Roch theorem. We describe the connection to the geometry of numbers of algebraic function elds and develop a notion and algorithm ...

We consider the problem of deciding whether a given rational function has a power series expansion with all its coefficients positive. Introducing an elementary transformation that preserves such positivity we are able to provide an elementary proof for the positivity of Szegö’s function 1 (1− x)(1− y)+ (1− y)(1− z)+ (1− z)(1− x) which has been at the historical root of this subject starting wi...