We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite di↵erence schemes. By studying the Fourier series expansions of the source discretization and the finite di↵erence operator, we derive su cient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in F...

The work of interval arithmetic was originally introduced by Dwyer [3] in 1951. The development of interval arithmetic as a formal system and evidence of its value as a computational device was provided by Moore [15] and Moore and Yang [16]. Furthermore, Moore and others [3]; [4]; [10] and [17] have developed applications to differential equations. Chiao in [2] introduced sequence of interval n...

The probability density for the solution yn of a stochastic di erence equation is considered. Following Knessl, Matkowsky, Schuss, and Tier [1] it is shown to satisfy a master equation, which is solved asymptotically for large values of the index n. The method is illustrated by deriving the large deviation results for a sum of independent identically distributed random variables and for the joi...

We present a multilevel high order ADI method for separable generalized Helmholtz equations. The discretization method we use is a 1-D fourth order compact nite di erence applied to each directional component of the Laplace operator, resulting a discrete system e ciently solvable by ADI methods. We apply this high order di erence scheme to all levels of grids, and then starting from the coarses...

Many compressible ow and aeroacoustic computations rely on accurate nonre ecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a nite-di erence scheme, the dispersive nature of the discretized equations can lead to spurious numerical re ections not seen in the continuous boundary value problem. Here we construct discretely nonre ecting bounda...

This paper analyses Rawls’s celebrated di¤erence principle, and its lexicographic extension, in societies with a …nite and an in…nite number of agents. A uni…ed framework of analysis is set up, which allows one to characterise Rawlsian egalitarian principles by means of a weaker version of a new axiom the Harm Principle recently proposed by [13]. This is quite surprising, because the Harm princ...

A …rst-order linear di¤erence system under rational expectations is, AEyt+1jIt = Byt +C(F)ExtjIt; where yt is a vector of endogenous variables; xt is a vector of exogenous variables; Eyt+1jIt is the expectation of yt+1 given date t information; and C(F)ExtjIt = C0xt+ C1Ext+1jIt + ::: + CnExt+njIt. Many economic models can be written in this form, especially if the matrix A is permitted to be si...

In this paper, the new set di§erence is deÖned between interval- ued intuitionistic fuzzy sets (IVIFSs).A di§erent perspective reduced to formal IVIFSs. This difference IVIFSs introduced by using : operation. Instead of comparing operator with all other operations, operation which defined \ used. Some fundamentel properties are provided and not on examined whether satisfy or alpha-operation. By...

We compare between the binary congestion indication scheme and the explicit rate indication scheme proposed for congestion control of ATM's available bit rate service (ABR). The fairness problems of the binary congestion indication scheme that arise when mixing long and short distance tra c are investigated. Our simulations suggest that the unfairness noticed in this case towards the long dista...

This chapter is dedicated to the de nition of relevant sets of shapes and that of de ning a metric on them. Following a recent research monograph by Delfour and Zolesio [33], we consider the characteristic functions of the subsets of R2 and their distance functions. The L2 norm of the di erence of characteristic functions, the L∞ and the W 1,2 norms of the di erence of distance functions de ne ...