The barotropic vorticity equation model is very important in the research of meteorological science and applied mathematics. Many scientists pay attention to the research of numerical methods of this equation. The early works were mainly concerned with finite difference methods [2, 4, 8, 9, 13]. The spectral method has a convergence rate of ”infinite” order, i.e., the error decays faster than a...

In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous-time optimal control problem, to a finite-dimensional constrained nonlinear programming problem. This resulting optimization probl...

We present a stable algorithm for constructing derivative matrices with small norm for pseudospectral methods. In particular, we construct second derivative matrices that incorporate Dirichlet or Neumann boundary conditions on an interval and on the disk. By construction, the norm of these matrices grows at the optimal rate O(N) for N -by-N matrices, in contrast to standard pseudospectral const...

Bratu's problem, which is the nonlinear eigenvalue equation Au + 2 exp(u)= 0 with u = 0 on the walls of the unit square and 2 as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance of symmett:v: because of invariance under the C 4 rotation group and parity in both x and y, one can slash the size of the basis set by a...

In the framework of mapped pseudospectral methods, we introduce a new polynomialtype mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the spectral interpolation error, the new polynomialtype mapping is compared against previously proposed mappings for the study of collapse and shock wave phenomena. As...

In this note the conditions used in proving a result due to S. M. Ross and H. M. Taylor are examined. These results pertain to the existence of bounded solutions to the average cost optimality equation for controlled Markov processes with an average cost criterion. In particular, we show how the use of commonly found convexity (concavity) properties of value functions can be employed to verify ...

A weighted orthogonal system on the half-line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...

A weighted orthogonal system on the half line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...

Two different numerical methods for solving a non-self-adjoint evolution equation are compared in this paper. If the initial function lies in the domain of the operator, a recently proposed method that combines pseudospectral ideas and semigroup theory is shown to be considerably more accurate than a standard discretization method. One example is worked out in detail, but the methods used are o...

Starting from the observation that a sentence like ??a dog is intelligent is difficult in the generic domain in the same way as ??a student is shy is in the existential one, this paper argues that as for the existential reading, the generic interpretation of the indefinites also needs a “context”. Adopting an explicit modal interpretation of GEN, our account builds on Greenberg (2002) insight t...