A third-order ordinary differential equationwith application in the flow of a thin liquid film is considered.The boundary conditions come from Tanner’s problem for the surface tension driven flow of a thin film. Symmetric and nonsymmetric finite difference schemes are implemented in order to obtain steady state solutions. We show that a central difference approximation to the third derivative i...

Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time der...

Let X be a compact metric space. By results of Brown, Douglas and Fillmore, [BDF2], the K-homology of X is realized by Ext(X), the equivalence classes of unital and essential extensions of C(X) by the compact operators K on a separable infinite dimensional Hilbert space H , or equivalently, the equivalence classes of unital and injective ∗-homomorphisms C(X) → Q, where Q = L(H)/K is the Calkin ...

In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are hi...

This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.

We obtain a general bound on the Turán density of a hypergraph in terms of the number of edges that it contains. If F is an r-uniform hypergraph with f edges we show that π(F) < f−2 f−1 − (1 + o(1))(2r!2/rf3−2/r)−1, for fixed r ≥ 3 and f → ∞. Given an r-uniform hypergraph F , the Turán number of F is the maximum number of edges in an r-uniform hypergraph on n vertices that does not contain a co...

In this paper, a new learning method is proposed to build Support Vector Machines (SVM) Binary Decision Function (BDF) of reduced complexity, efficient generalization and using an adapted hybrid color space. The aim is to build a fast and efficient SVM classifier of pixels. The Vector Quantization (VQ) is used in our learning method to simplify the training set. This simplification step maps pi...

Moving-grid methods are becoming increasingly popular for solving several kinds of parabolic and hyperbolic partial differential equations involving fine-scale structures such as steep moving fronts and emerging steep layers. An interesting example of such a method is provided by the moving-finite-element (MFE) method. A difficulty with MFE, as with many other existing moving-grid methods, is t...

Recently Ch. Lubich proved convergence results for Runge-Kutta methods applied to stii mechanical systems. The present paper discusses the new ideas necessary to extend these results to general linear methods, in particular BDF and multistep Runge-Kutta methods. Stii mechanical systems arise in the modelling of mechanical systems containing strong springs and (or) elastic joints. A typical exam...

A new BDF-type scheme is proposed for the numerical integration of the system of ordinary differential equations that arises in the Method of Lines solution of time-dependent partial differential equations. This system is usually stiff, so it is desirable for the numerical method to solve it to have good properties concerning stability. The method proposed in this article is almost L-stable and...