In this paper, a class of A()-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number and stiffly stable for and . Some numerical results are reported to illustrate the method.
Following the -convergence approach introduced by Müller and Ortiz, the convergence of discrete dynamics for lagrangians with quadratic behavior is established.
Following the Γ-convergence approach introduced by Müller and Ortiz, the convergence of discrete dynamics for Lagrangians with quadratic behavior is established.
Abelovu cenu získala v roce 2019 matematička Karen Uhlenbecková. Její práce mají důležitý dopad hned na několik oborů matematiky - geometrii, analýzu i matematickou fyziku. Zásadním způsobem ovlivnila moderní pojetí geometrické analýzy. V článku se pomocí relativně jednoduchých příkladů snažíme čtenáře seznámit se dvěma z oblastí, kterými se doposud zabývala. Na závěr též velmi stručně zmiňujeme hlavní výsledky několika jejích prací.
The starting point of the analysis in this paper is the following situation: “In a bounded domain in , let a finite set of points be given. A triangulation of that domain has to be found, whose vertices are the given points and which is ‘suitable’ for the linear conforming Finite Element Method (FEM).” The result of this paper is that for the discrete Poisson equation and under some weak additional assumptions, only the use of Delaunay triangulations preserves the maximum principle.