Robustness of computations in engineering is one of key issues as it is necessary to solve technical problems leading to ill conditioned solutions. Therefore the robustness and numerical stability is becoming a key issue more important that the computational time. In this paper we will show selected computational issues in numerical precision, well known cases of failures in computations. The E...

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these...

In this paper, an optimal stable algorithm is presented for members of a robots swarm moving toward a target. Equations of motion of the swarm are based on Lagrangian energy equations. Regarding of similar research On the design of swarm motion algorithm, an equation of motion considered constraints to guarantee no collision between the members and the members and obstacles along the motion pat...

We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein coordinates. The simplicity of the system allow to display and deal with the typical gauge instability present in these coordinates. The numerical evolution ...

We consider complex Fenchel–Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra’s plumbing construction and are related to earthquakes on Teichmüller space. They also allow us to interpolate between two coordinate systems on Teichmüller space, namely the classical Fuchsian space with Fenchel–Nielsen coordinates and the Maskit e...

A, et al. Nonlinear analysis of electroencephalogram at rest and during cognitive tasks in patients with schizophrenia. One-dimensional electroencephalography (EEG) data were transformed into multidimensional phase space. The phase space concept is crucial for nonlinear dynamics analysis. In a hypothetical system governed by n variables, the phase space is n-dimensional. Each state of the syste...