A new method Is presented for determining the moments of nuclear magnetic resonance absorption lines from the shape of either the free Induction decay or that of the echo. Unlike previously used techniques, this method does not require the assumption of an analytical function for the lineshape or the fitting of the experimental decay with a polynomial. A fast, suitably precise and numerically s...

This note describes a numerically stable procedure to derive a canonical coordinate system for a 2D linear transformation. The determinant of the transformation from the given coordinate system to the canonical coordinate system is 1; thus area is preserved. The transformation is composed of a short sequence of rotations and areapreserving nonuniform scales. If the eigenvectors are real, they m...

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.

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...

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9-dimensional submanifold of the 12-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This freedom...