We design, analyse and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media. The discretisation is based on several adaptations of the Hybrid-High-Order (HHO) method due to Di Pietro et al. [Computational Methods in Applied Mathematics, 14(4), (2014)]. The equation governing the pressure is ...

Neville’s algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.

Transparent boundary conditions (TBCs) for general Schrr odinger{ type equations on a bounded domain can be derived explicitly under the assumption that the given potential V is constant on the exterior of that domain. In 1D these boundary conditions are non{local in time (of memory type). Existing discretizations of these TBCs have accuracy problems and render the overall Crank{Nicolson nite d...

The accuracy of atomistic-to-continuum hybrid methods can be guaranteed only for deformations where the lattice configuration is stable for both the atomistic energy and the hybrid energy. For this reason, a sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation of lattice defects. We formulate a simple one...

We analyze numerical stability of a recursive computation scheme of present value (PV) amd show that the absolute error increases exponentially for positive discount rates. We show that reversing the direction of calculations in the recurrence equation yields a robust PV computation routine.

We consider the numerical computation of stationary distributions for level dependent quasi-birth-and-death processes. An algorithm based on matrix continued fractions is presented and compared to standard solution techniques. Its computational efficiency and numerical stability is demonstrated by numerical examples.

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is studied. The applications of these filters include processing video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The GR model is embedded into the second model of Fornasini-Marchesisni (FM) and the stability of th...

In this paper, we give a numerically reliable algorithm to compute the zeros of a periodic descriptor system. The algorithm is a variant of the staircase algorithm applied to the system pencil of an equivalent lifted time-invariant state-space system and extracts a low-order pencil which contains the zeros (both 6nite and in6nite) as well as the Kronecker structure of the periodic descriptor sy...

This note considers the stability of uncertain matrices. It is shown that under certain structural assumptions on the uncertain matrices the Schur stability can be assured from computing the numerical radius of the vertex matrices. This result is less conservative than that of using a simultaneous Lyapunov function method. Necessary and sufficient conditions are also obtained for the stability ...

We show that L 4 and L 5 in the spatial restricted circular three{body problem are Nekhoroshev{ stable for all but a few values of the reduced mass up to the Routh critical value. This result is based on two extensions of previous results on Nekhoroshev{stability of elliptic equilibria, namely to the case of`directional quasi{convexity', a notion introduced here, and to a (non-convex) steep cas...