Variational formulations of time-dependent PDEs in space and time yield (d + 1)-dimensional problems to be solved numerically. This increases the number unknowns as well storage amount. On other hand, this approach enables adaptivity model reduction w.r.t. both type variables. In paper, we show that matrix oriented techniques can significantly reduce computational timings for solving arising li...

In this issue, instead of a review new books or textbooks on transport and transportation, paying tribute to the oeuvres our predecessors, journal reproduces bibliographic article first appeared more than century ago in «Zheleznodorozhnoe delo» [Rail Business]. The editors hope that it will help get an idea how concise, meaningful and, modern terms, informative reviews scientific literature wer...

Modifications to the standard finite element mass matrix are considered with the aim of preserving the positivity of the discrete solution. The approach is used in connection with calculating the initial time derivative values for parabolic equations and in connection with nonlinear Petrov-Galerkin schemes for hyperbolic equations in one space dimension. The extension of the ideas to unstructur...

We develop further the integration procedure in the generalised invariant formalism , and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A ...