In this article the numerical approximation of solutions of Itô stochastic differential equations is considered, in particular for equations with a small parameter 2 in the noise coefficient. We construct stochastic linear multi-step methods and develop the fundamental numerical analysis concerning their mean-square consistency, numerical stability in the mean-square sense and mean-square conve...

In this paper, the gradient vector flow fields are introduced in the image anisotropic diffusion, and the shock filter, mean curvature flow and Perona-Malik equation are reformulated respectively in the context of this flow fields. Many advantages over the original models can be obtained, such as numerical stability, a large capture range, and computational simplification etc. In addition, the ...

The advent of supercomputers with hierarchical memory systems has imposed the use of block algorithms for the linear algebra algorithms. Although block algorithms may result in impressive improvements in performance, their numerical properties are quite different from their scalar counterpart and deserve an in-depth study. In this paper, the numerical stability ofblock Gram-Schmidt orthogonaliz...

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the newmethod are given and the efficiency of the newmethod is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-or...

Many important scientiic problems can be formulated as systems of ordinary diieren-tial equations with two-point boundary value constraints (BVODE). Multiple shooting is one of the most widely used numerical techniques for solving BVODE problems. In this work, we present a new distributed parallel numerical algorithm for BVODEs which is based on multiple shooting. We investigate the numerical s...

In geometric modelling surfaces can be given essentially in two ways: implicit and parametric form. The automatic transition between the implicit and the parametric representations of surfaces is of fundamental importance. In the literature there are several symbolic/numeric implicitization techniques based on resultants [1], Gröbner–basis [2], moving surfaces [3], linear algebra [4], but the n...

The isentropic gas dynamics equations in Eulerian coordinates are expressed by means of the density p and the momentum q = pu, instead of the velocity u, in order to get domains bounded and invariant in the (p. <?)-plane, for a wide class of pressure laws p(p) and in the monodimensional case. A numerical scheme of the transport-projection type is proposed, which builds an approximate solution v...

Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial differential equations often hinges on capturing subtle aspects of the structure of the system in the discretization. In many cases the differential geometric...

This paper presents stability results for various fast trigonometric transforms. We consider the numerical stability of the classical fast Fourier transform (FFT) with respect to diierent precomputation methods for the involved twiddle factors and show the strong innuence of precomputation errors on the numerical stability of the FFT. The examinations are extended to fast algorithms for the com...