Preface to the Focused Issue on High-Order Numerical Methods for Evolutionary PDEs

Preface: DGAA Special Issue on Numerical Methods for Dynamic Games

The theory of dynamic games has progressed very much in the last decades, and these models are now used in many areas which span from economics to engineering applications, from decisionmodels in social sciences to computer science. Just to quote two typical examples, the allocation of investments in dynamic industry models or the optimal policy design in (multicountry) macroeconomic settings c...

Preface to the special issue "High order methods for CFD problems"

Since a few years, there has been a renew in interest in (very) high order schemes for compressible fluid dynamics for steady and unsteady problems. Within Europe and the US, several conferences deal with these issues, some of them have been launched only recently. Several special issues of recent or future AIAA conferences are specially devoted to that topic. The goal of these researches is to...

Numerical Methods for PDEs

Numerical Methods for PDEs

Some high-order Taylor-models based methods for solving PDEs

We present three different approaches to solving PDEs based Taylor-models. In each approach we stress a high accuracy which can be achieved with a grid of relatively low-order Taylor polynomials. In particular, in solving Dirichlet boundary problem for the Laplace equation with the grid of step h of quadratic Taylor polynomials we get the discretization error of order h^10. Similar results are ...