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...

The 3D Laplace equation is one of the important PDEs of physics and describes the phenomonology of electrostatics and magnetostatics. Frequently very precise solution of this PDE is required; but with conventional finite element or finite difference codes this is difficult to achieve because of the need for an exceedingly fine mesh which leads to often prohibitive CPU time. We present an altern...

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 ...

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exi...

The concept of topological sensitivity has been successfully employed as an imaging tool to obtain the correct initial topology and preliminary geometry of hidden obstacles for a variety of inverse scattering problems. In this paper, we extend these ideas to acoustic scattering involving transient waveforms and penetrable obstacles. Through a boundary integral equation framework, we present a d...

Effects of wall material on the channel capacity of an indoor multiple input multiple output (MIMO) system are investigated using a hybrid technique of the method of moments (MoM) and the finite difference time domain (FDTD) method with consideration of the Ricean K factor and the effective degrees of freedom (EDOF) of multiple paths. key words: MIMO, channel capacity, indoor channel, hybrid me...