We develop in this paper a numerical method to simulate three-dimensional incompressible flows based on a decomposition of the flow into an axisymmetric part, in terms of the stream function and the circulation, and a non-axisymmetric part in terms of a potential vector function. The method is specially suited for the study of nonlinear stability of axially symmetric flows because one may follo...

The unsteady heat, mass, and fluid transfer over a horizontal stretching sheet has been numerically investigated. Using a similarity transformation the governing time-dependent boundary layer equations for the momentum, heat, and mass transfer were reduced to a sets of ordinary differential equations. These set of ordinary differential equations were then solved using the Chebyshev pseudo-spect...

Seismic modeling is a foundation of geophysical date processing. A multisymplectic pseudospectral method for seismic modeling is presented in this paper. This method takes the multisymplectic structure of the scalar wave equation into account and possesses discrete multisymplectic conservation laws. Numerical experiments demonstrate the remarkable capability of this new method for long-time sim...

In this paper, we give a characterization of the visibility graphs of pseudo-polygons. We first identify some key combinatorial properties of pseudo-polygons, and we then give a set of five necessary conditions based off our identified properties. We then prove that these necessary conditions are also sufficient via a reduction to a characterization of vertex-edge visibility graphs given by O’R...

Human head movement can be looked at, as a rotational dynamics on the space SO(3) with constraints that have to do with the axis of rotation. Typically the axis vector, after a suitable scaling, is assumed to lie in a surface called Donders’ surface. Various descriptions of Donders’ surface are in the literature and in this paper we assume that the surface is described by a quadratic form. We p...

in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

A numerical algorithm for effective incorporation of parametric uncertainty into mathematical models is presented. The uncertain parameters are modeled as random variables, and the governing equations are treated as stochastic. The solutions, or quantities of interests, are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters. A high-order s...