An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method’s weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we st...

Extrapolation methods for the solution of partial diierentialequations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as-extrapolation. For nite e...

A family of explicit space-time finite element methods for the initial boundary value problem for linear, symmetric hyperbolic systems of equations is described and analyzed. The method generalizes the discontinuous Galerkin method and, as is typical for this method, obtains error estimates of order O(hn+1/2) for approximations by polynomials of degree ≤ n.

We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stabl...

Using cultured human umbilical vein endothelial cells, in which phosphatidylcholine (PC) is equally pulse-labelled by various eicosanoid precursor fatty acids (EPFAs), we have studied the remodelling of EPFAs among the phospholipid classes and subclasses with and without activation, and the relationship of this remodelling process to the selective release of arachidonic acid (AA) by phospholipa...

Introduction Implicit attitudes are preferences that exist outside of conscious awareness or conscious control. Recent evidence demonstrates that these preferences are variably related to selfreported (explicit) measures of preference. For example, Nosek, Banaji, & Greenwald (in press; Group Dynamics) showed that correspondence between implicit and explicit measures partially depends on the tar...

Fredholm determinant asymptotics of convolution operators on large finite intervals with rational symbols having real zeros are studied. The explicit asymptotic formulae obtained can be considered as a direct extension of the Ahiezer-Kac formula to symbols with real zeros.

We present an explicit method to evaluate the nonnegativity of order 3 Matrix exponential functions.

Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using combination of two-colour and five-colour symmetries. Here we present explicit constructions of several of the predicted colourings for the first time, and disc...