ABSTRACT High order nite di erence WENO methods have the advantage of simpler coding and smaller computational cost for multi-dimensional problems, compared with nite volume WENO methods of the same order of accuracy. However a main restriction is that conservative nite di erence methods of third and higher order of accuracy can only be used on uniform rectangular or smooth curvilinear meshes. ...

This paper describes a new symmetry-based approach to solving a given ordinary di¬erence equation. By studying the local structure of the set of solutions, we derive a systematic method for determining one-parameter Lie groups of symmetries in closed form. Such groups can be used to achieve successive reductions of order. If there are enough symmetries, the di¬erence equation can be completely ...

Dynamic load balancing on hypercube multiprocessors is considered with emphasis on quantized loads. Quantized loads are divisible only in a xed size. First, we show that a direct application of the well-known Dimension Exchange Method(DEM) to quantized loads may result in di erence in assigned loads to processors as large as logN units after balancing for a hypercube of size N . Then we propose...

Voronoi cells and the notion of natural neighbours are used to develop a nite di erence method for the di usion operator on arbitrary unstructured grids. Natural neighbours are based on the Voronoi diagram, which partitions space into closest-point regions. The Sibson and the Laplace (non-Sibsonian) interpolants which are based on natural neighbours have shown promise within a Galerkin framewor...

This paper proposes a solution method to solve linear di¤erence models with lagged expectations in the form of

We introduce a new method to obtain pointwise error estimates for vanishing viscosity and nite di erence approximations of scalar conservation laws with piecewise smooth solutions. This method can deal with nitely many shocks with possible collisions. The key ingredient in our approach is an interpolation inequality between the L and Lip-bounds, which enables us to convert a global result into ...

Linear stability analysis of the three dimensional plane wake flow is performed using a mapped finite di?erence scheme in a domain which is doubly infinite in the cross–stream direction of wake flow. The physical domain in cross–stream direction is mapped to the computational domain using a cotangent mapping of the form y = ?cot(??). The Squire transformation [2], proposed by Squire, is also us...

In this paper implementations of three numerical schemes for the numerical simulation of the complex modi ed Korteweg de Vries CMKdV equation are reported The rst is an integrable scheme derived by methods related to the Inverse Scattering Transform IST The second is derived from the rst and is called the local IST scheme The third is a standard nite di erence scheme for the CMKdV equation Trav...

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...

When one considers the e ect in the physical space, Daubechies-based wavelet methods are equivalent to nite di erence methods with grid re nement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coe cient is, essentially, equivalent to adding a grid point, or two, at the same ...