As computational performance becomes more readily available, there will be an increasing variety of interactive graphical applications with iterative numerical techniques at their core. In this paper, we consider how to support the unique demands of such applications. In particular, we focus on how to set up the numerical problems which must be solved. In the context of interactive systems, thi...

It is well known that a D-string ending on a D3, D5 or D7 brane is described in terms of a non-commutative fuzzy funnel geometry. In this article, we give a numerical study of the fluctuations about this leading geometry. This allows us to investigate issues related to the stability and moduli space of these solutions. We comment on the comparison to the linearized fluctuations in supergravity.

It has been the standard teaching of today that backward stability analysis is taught as absolute, just as in Newtonian physics time is taught as absolute time. We will prove that it is not true in general. It depends on algorithms. We will prove that forward and mixed stability analysis are absolutely invalid stability analysis in the sense that they have absolutely wrong reference points for ...

In this paper we present error estimates for the ®nite element approximation of Poisson and modi®ed Helmholtz equations outside an obstacle or in a semi-in®nite strip in the plane. The ®nite element approximation is formulated on a bounded domain using a local approximate arti®cial boundary condition. In fact there is a sequence of local approximate boundary conditions for a given arti®cial bou...

We study, in this work, the maximum principle for the Beltrami color flow and the stability of the flow’s numerical approximation by finite difference schemes. We discuss, in the continuous case, the theoretical properties of this system and prove the maximum principle in the strong and the weak formulations. In the discrete case, all the second order explicit schemes, that are currently used, ...

We study, in this work, the maximum principle for the Beltrami color flow and the stability of the flow’s numerical approximation by finite difference schemes. We discuss, in the continuous case, the theoretical properties of this system and prove the maximum principle in the strong and the weak formulations. In the discrete case, all the second order explicit schemes, that are currently used, ...

The thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid in the presence of uniform vertical magnetic field is considered. For the case of stationary convection, Rivlin-Ericksen viscoelastic fluid behaves like a Newtonian fluid. It is found that rotation has a stabilizing effect, whereas the magnetic field has both stabilizing and destabilizing effects. Graphs have been plotted ...

We derive a new algorithm for computing the action f(A)V of the cosine, sine, hyperbolic cosine, and hyperbolic sine of a matrix A on a matrix V , without first computing f(A). The algorithm can compute cos(A)V and sin(A)V simultaneously, and likewise for cosh(A)V and sinh(A)V , and it uses only real arithmetic when A is real. The algorithm exploits an existing algorithm expmv of Al-Mohy and Hi...

The manner in which sma.ll perturbations in the data give rise to a perturbation in the solution of a two point. boundary value problem will determine how effectively the solution can be approximated nmnerically. However ·this 'conditioning' also has a number of other implications that are less obvious. 'rhese include the effec·t on the stability of numerical schemes, the condi·tioning of shoot...