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Convergence and stability constant of the theta-method

Faragó, István (2013)

Applications of Mathematics 2013

The Euler methods are the most popular, simplest and widely used methods for the solution of the Cauchy problem for the first order ODE. The simplest and usual generalization of these methods are the so called theta-methods (notated also as θ -methods), which are, in fact, the convex linear combination of the two basic variants of the Euler methods, namely of the explicit Euler method (EEM) and of the implicit Euler method (IEM). This family of the methods is well-known and it is introduced almost...

Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability

Kůs, Pavel (2015)

Application of Mathematics 2015

In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problem are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.

Conversion of TeX Documents to PDF

Pejović, Aleksandar, Mijajlović, Žarko (2009)

Towards a Digital Mathematics Library. Grand Bend, Ontario, Canada, July 8-9th, 2009

We discuss in some detail some of the drawbacks of PDF files obtained from mathematical papers prepared in TeX, particularly concerning indexing, copy/paste and OCR capabilities.

Counting triangles that share their vertices with the unit n -cube

Brandts, Jan, Cihangir, Apo (2013)

Applications of Mathematics 2013

This paper is about 0 / 1 -triangles, which are the simplest nontrivial examples of 0 / 1 -polytopes: convex hulls of a subset of vertices of the unit n -cube I n . We consider the subclasses of right 0 / 1 -triangles, and acute 0 / 1 -triangles, which only have acute angles. They can be explicitly counted and enumerated, also modulo the symmetries of I n .

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