A (v, k, λ) difference family ((v, k, λ)-DF in short) over an abelian group G of order v is a collection F = {Bi | i ∈ I} of k-subsets of G, called base blocks, such that each nonzero element of G can be represented in precisely λ ways as a difference of two elements lying in some base blocks in F . A disjoint (v, k, λ)-DF is a difference family with disjoint blocks. In this paper, it is proved...

In discussing finite difference methods for the solution of hyperbolic par t ia l differential equations, STETrER [1] used est imates on some absolutely convergent Fourier series to prove stabi l i ty and instabi l i ty with respect to uniform convergence. I f / , a complex valued function on the circle, has an absolutely convergent Fourier series, then the n-th power of ] also has an absolutel...

Strong external difference family (SEDF) and its generalizations GSEDF, BGSEDF in a finite abelian group G are combinatorial designs raised by Paterson and Stinson [7] in 2016 and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using differe...

The convergence of a class of combined spectral-finite difference methods using Hermite basis, applied to the Fokker-Planck equation, is studied. It is shown that the Hermite based spectral methods are convergent with spectral accuracy in weighted Sobolev space. Numerical results indicating the spectral convergence rate are presented. A velocity scaling factor is used in the Hermite basis and i...

In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We prove that the numerical approximation...

In the semiclassical regime, solutions to the time-dependent Schrödinger equation are highly oscillatory. The number of grid points required for resolving the oscillations may become very large even for simple model problems, making solution on a grid, e.g., using a finite difference method, intractable. Asymptotic methods like Gaussian beams can resolve the oscillations with little effort and ...