This paper is concerned with the numerical solution of implicit neutral functional diierential equations. Based on the continuous Runge{Kutta method (for ordinary diierential equations) and the collocation method (for functional equations), two general one-step methods are formulated and their uniform order of approximation are discussed. Numerical stability of a class of Runge{Kutta-Collocatio...

Synopsis The failure of landslide dam formed by mass movements may occur by sudden sliding of the dam body. So, this study focuses on three-dimensional (3D) transient seepage and slope stability analysis of landslide dam. The 3D slope stability model coupled with transient seepage flow model is used for numerical simulations. Experiments are performed in the flume to measure movement of moistur...

We consider residual-based stabilised finite element methods for the generalised Oseen problem. The unique solvability based on a modified stability condition and an error estimate are proved for inf-sup stable discretisations of velocity and pressure. The analysis highlights the role of an additional stabilisation of the incompressibility constraint. It turns out that the stabilisation terms o...

In this paper, we propose and numerically investigate a family of locally divergence-free central discontinuous Galerkin methods for ideal magnetohydrodynamic (MHD) equations. The methods are based on the original central discontinuous Galerkin methods (SIAM Journal on Numerical Analysis 45 (2007) 2442-2467) for hyperbolic equations, with the use of approximating functions that are exactly dive...

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of Ω( √ n) on th...

In this paper we study the eigenvalues of a matrix S which arises in the recovery of lost samples from oversampled band-limited signals. Emphasis is placed on the variation of the eigenvalues as a function of the distribution of the missing samples and as a function of the oversampling parameter. We present a number of results which help to understand the numerical difficulties that may occur i...

This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in numerical instability due to division by zero. We propose a variation on the flow that removes the numerical instability in the discretization and show that this modification res...

This paper introduces a new class of methods, which we call Möbius schemes, for the numerical solution of matrix Riccati differential equations. The approach is based on viewing the Riccati equation in its natural geometric setting, as a flow on the Grassmanian of m-dimensional subspaces of an (n + m)-dimensional vector space. Since the Grassmanians are compact differentiable manifolds, and the...

For the numerical solution of stochastic differential equations explicit economical three-stage Runge-Kutta schemes of weak second order have been proposed in a previous work. Here numerical stability of these methods is studied and some examples are presented to support the theoretical results. Mathematics Subject Classification: 60H10

This paper gives perturbation analyses for the Cholesky factorization A = R T R of a real symmetric positive deenite matrix A, with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations on nite precision oating point computers. First-order and rigorous perturbation bounds are are obtained. The analyses more accurately re...