The finite-difference-time-domain (FDTD), although recognized as a flexible, robust and simple to implement method for solving complex electromagnetic problems, is subject to numerical dispersion errors. In addition to the traditional ways for reducing dispersion, i.e., increasing sampling rate and using higher order degrees of accuracy, a number of schemes have been proposed recently. In this ...

We develop a new high order accurate time-discretisation technique for initial value problems. We focus on problems that originate from a space discretisation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new timediscretisation method is global and together with the approximation in space, i...

The energy of solutions of the wave equation with a suitable boundary dissipation decays exponentially to zero as time goes to infinity. We consider the finite-difference space semi-discretization scheme and we analyze whether the decay rate is independent of the mesh size. We focus on the one-dimensional case. First we show that the decay rate of the energy of the classical semi-discrete syste...

In this paper, a numerical solution for a system of singularly perturbed convection-diffusion equations is studied. The system is discretized by the Il’in scheme on a uniform mesh. It is proved that the numerical scheme has first order accuracy, which is uniform with respect to the perturbation parameters. We show that the condition number of the discrete linear system obtained from applying th...

A 3-D model for atmospheric pollutant transport is proposed considering a set of coupled convection–diffusion–reaction equations. The convective phenomenon is mainly produced by a wind field obtained from a 3-D mass consistent model. In particular, the modelling of oxidation and hydrolysis of sulphur and nitrogen oxides released to the surface layer is carried out by using a linear module of ch...

In this paper we investigate the Mimetic Finite Difference method for the approximation of a constraint optimal control problem governed by an elliptic operator. A priori error estimates of the first order are derived in suitable discrete norms for both the control and the state variables. The theoretical results are confirmed by numerical experiments performed on a set of test cases selected f...

In this article, a numerical study for the fractional wave equations is introduced by using a class of finite difference methods. These methods are extension of the weighted average methods for ordinary (non-fractional) wave equations. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. Simple and ...

We develop a simple energy method for proving the stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. In particular, we extend to several space dimensions and to variable coefficients a crucial stability result by Goldberg and Tadmor for Dirichlet boundary conditions. This allows us to give some conditions on the discretized operator that ensu...

We analyze finite difference methods for the Gross-Pitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate, for the conservative Crank-Nicolson finite difference (CNFD) method and semi-implicit finite difference (SIFD) method, at the order of O(h2 + τ2) in the l2-norm and discrete H1-norm with time step τ and mesh size h. Be...

We consider a rating-based model for the term structure of credit risk spreads wherein the creditworthiness of the issuer is represented as a finite-state continuous time Markov process. This approach entails a progressive drift in credit quality towards default. A model of the economy is presented featuring stochastic transition probabilities; credit instruments are valued via an ultra parabol...