Two-level linearized and local uncoupled difference schemes for the two-component evolutionary Korteweg-de Vries system

The two-level linearized and local uncoupled spatial second order and compact difference schemes are derived for the two-component evolutionary system of nonhomogeneous Korteweg-de Vries equations. It is shown by the mathematical induction that these two schemes are uniquely solvable and convergent in a discrete L_∞ norm with the convergence order of O(τ² + h²) and O(τ² + h⁴), respectively, where τ and h are the step sizes in time and space. Three numerical examples are given to confirm the theoretical results.     

Ideal ramp schemes and augmented orthogonal arrays

Ramp schemes were invented in 1985 by C.R. Blakley and C. Meadows. An $(s,t,n)$-ramp scheme is a generalization of a threshold scheme in which there are two thresholds. Recently, D.R. Stinson established the equivalence of ideal ramp schemes and augmented orthogonal arrays. In this study, some new construction methods for augmented orthogonal arrays are presented and then some new augmented orthogonal arrays are obtained; furthermore, we also provide parameter situations where ideal ramp schemes exist for these obtained augmented orthogonal arrays.     

Car path tracking in traffic flow networks with bounded buffers at junctions

This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at junctions that allow for the interpretation of roundabouts or on-ramps while the traffic dynamics is based on first-order macroscopic equations of Lighthill-Whitham-Richards (LWR) type. Trajectories for single drivers are then influenced by the surrounding traffic and can be tracked by appropriate numerical algorithms. The computational experiments show how the modeling framework can be used as navigation device.     

Generalized wreath products of table algebras determined by their character tables and applications to association schemes

Structures of table algebras whose character tables have a zero submatrix were studied in Blau and Xu (2014) and Chen and Xu (2018). In this paper we continue the research in this direction, and investigate the conditions under which the character table with a zero submatrix yields a generalized wreath product of table algebras. Applications to association schemes are also discussed.     

On the gonality of stable curves

In this paper we use admissible covers to investigate the gonality of a stable curve C over $\mathbb{C}$. If C is irreducible, we compare its gonality to that of its normalization. If C is reducible, we compare its gonality to that of its irreducible components. In both cases we obtain lower and upper bounds. Furthermore, we show that four admissible covers constructed give rise to generically injective maps between Hurwitz schemes. We show that the closures of the images of three of these maps are components of the boundary of the target Hurwitz schemes, and the closure of the image of the remaining map is a component of a certain codimension‐1 subscheme of the boundary of the target Hurwitz scheme.     

Staggered discontinuous Galerkin methods for the incompressible Navier–Stokes equations: Spectral analysis and computational results

The goal of this paper is to create a fruitful bridge between the numerical methods for approximating PDEs in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear systems. Among the main objectives are the design of new, efficient iterative solvers and a rigorous analysis of their convergence speed. The link we have in mind is either the structure or the hidden structure that the involved coefficient matrices inherit, both from the continuous PDE and from the approximation scheme; in turn, the resulting structure is used for deducing spectral information, crucial for the conditioning and convergence analysis and for the design of more efficient solvers. As a specific problem, we consider the incompressible Navier–Stokes equations; as a numerical technique, we consider a novel family of high‐order, accurate discontinuous Galerkin methods on staggered meshes, and as tools, we use the theory of Toeplitz matrices generated by a function (in the most general block, the multilevel form) and the more recent theory of generalized locally Toeplitz matrix sequences. We arrive at a somehow complete picture of the spectral features of the underlying matrices, and this information is employed for giving a forecast of the convergence history of the conjugate gradient method, together with a discussion on new and more advanced techniques (involving preconditioning, multigrid, multi‐iterative solvers). Several numerical tests are provided and critically illustrated in order to show the validity and the potential of our analysis.     

Assessment of WENO schemes for multi‐dimensional Euler equations using GPU

This paper presents a detailed study on the implementation of Weighted Essentially Non‐Oscillatory (WENO) schemes on GPU. GPU implementation of up to ninth‐order accurate WENO schemes for the multi‐dimensional Euler equations of gas dynamics is presented. The implementation detail is discussed in the paper. The computational times of different schemes are obtained and the speedups are reported for different number of grid points. Furthermore, the execution times for the main kernels of the code are given and compared with each other. The numerical experiments show the speedups for the WENO schemes are very promising especially for fine grids. Copyright © 2014 John Wiley & Sons, Ltd.     

Randomly changing leader-following consensus control for Markovian switching multi-agent systems with interval time-varying delays

This paper considers the problem of leader-following consensus stability and also stabilization for multi-agent systems with interval time-varying delays. The randomly occurring interconnection information of the leader and the Markovian switching interconnection information of the agent are matters of concern in the systems. Through construction of a suitable Lyapunov–Krasovskii functional and utilization of the reciprocally convex approach, new delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by using various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

A hybrid kinetic WENO scheme for inviscid and viscous flows

In this paper, we propose a high‐order finite volume hybrid kinetic Weighted Essentially Non‐Oscillatory (WENO) scheme for inviscid and viscous flows. Based on the WENO reconstruction technique, a hybrid kinetic numerical flux is introduced for the present method, which includes the mechanisms of both the free transfer and the collision of gas molecules. The collisionless free transfer part of the hybrid numerical flux is constructed from the conventional kinetic flux vector splitting treatment, and the collision contribution is considered by constructing an equilibrium gas state and calculating the corresponding numerical flux at the cell interface. The total variation diminishing Runge–Kutta methods are used for the temporal integration. The high‐order accuracy and good shock‐capturing capability of the proposed hybrid kinetic WENO scheme are validated by many numerical examples in one‐dimensional and two‐dimensional cases. Copyright © 2015 John Wiley & Sons, Ltd.