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Strategies for computation of Lyapunov exponents estimates from discrete data

Fischer, Cyril, Náprstek, Jiří (2019)

Programs and Algorithms of Numerical Mathematics

The Lyapunov exponents (LE) provide a simple numerical measure of the sensitive dependence of the dynamical system on initial conditions. The positive LE in dissipative systems is often regarded as an indicator of the occurrence of deterministic chaos. However, the values of LE can also help to assess stability of particular solution branches of dynamical systems. The contribution brings a short review of two methods for estimation of the largest LE from discrete data series. Two methods are analysed...

Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity

Victor A. Kovtunenko, Ján Eliaš, Pavel Krejčí, Giselle A. Monteiro, Judita Runcziková (2023)

Archivum Mathematicum

A long-time dynamic for granular materials arising in the hypoplastic theory of Kolymbas type is investigated. It is assumed that the granular hardness allows exponential degradation, which leads to the densification of material states. The governing system for a rate-independent strain under stress control is described by implicit differential equations. Its analytical solution for arbitrary inhomogeneous coefficients is constructed in closed form. Under cyclic loading by periodic pressure, finite...

Strong convergence estimates for pseudospectral methods

Wilhelm Heinrichs (1992)

Applications of Mathematics

Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.

Strong singularities in mixed boundary value problems

Irena Rachůnková (2006)

Mathematica Bohemica

We study singular boundary value problems with mixed boundary conditions of the form ( p ( t ) u ' ) ' + p ( t ) f ( t , u , p ( t ) u ' ) = 0 , lim t 0 + p ( t ) u ' ( t ) = 0 , u ( T ) = 0 , where [ 0 , T ] . We assume that 2 , f satisfies the Carathéodory conditions on ( 0 , T ) × p C ...

Structural Evolution of the Taylor Vortices

Tian Ma, Shouhong Wang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We classify in this article the structure and its transitions/evolution of the Taylor vortices with perturbations in one of the following categories: a) the Hamiltonian vector fields, b) the divergence-free vector fields, and c). the solutions of the Navier-Stokes equations on the two-dimensional torus. This is part of a project oriented toward to developing a geometric theory of incompressible fluid flows in the physical spaces.

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