Search results for "Numerical integration"

Coupled Discrete Fractional-Order Logistic Maps

2021

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.

A characterization of the distribution of a weighted sum of gamma variables through multiple hypergeometric functions

2008

Applying the theory on multiple hypergeometric functions, the distribution of a weighted convolution of Gamma variables is characterized through explicit forms for the probability density function, the distribution function and the moments about the origin. The main results unify some previous contributions in the literature on nite convolution of Gamma distributions. We deal with computational aspects that arise from the representations in terms of multiple hypergeometric functions, introducing a new integral representation for the fourth Lauricella function F (n) D and its con uent form (n) 2 , suitable for numerical integration; some graphics of the probability density function and distr…

A new method for computing one-loop integrals

1994

We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point functions both algebraically and numerically to all tensor cases. This program is written as a package for Maple. An additional Mathematica version is planned later.

On the dynamics of non-local fractional viscoelastic beams under stochastic agencies

2018

Abstract Non-local viscoelasticity is a subject of great interest in the context of non-local theories. In a recent study, the authors have proposed a non-local fractional beam model where non-local effects are represented as viscoelastic long-range volume forces and moments, exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants. Long-range interactions have been given a fractional constitutive law, involving the Caputo's fractional derivative. This paper introduces a comprehensive numerical approach to calculate the stochastic response of the non-local fractional beam model under Gaussian white no…

Drilling Systems: Stability and Hidden Oscillations

2013

There are many mathematical models of drilling systems Despite, huge efforts in constructing models that would allow for precise analysis, drilling systems, still experience breakdowns. Due to complexity of systems, engineers mostly use numerical analysis, which may lead to unreliable results. Nowadays, advances in computer engineering allow for simulations of complex dynamical systems in order to obtain information on the behavior of their trajectories. However, this simple approach based on construction of trajectories using numerical integration of differential equations describing dynamical systems turned out to be quite limited for investigation of stability and oscillations of these s…

Characterizing cavities in model inclusion molecules: a comparative study

1998

We have selected fullerene-60 and -70 cavities as model systems in order to test several methods for characterizing inclusion molecules. The methods are based on different technical foundations such as a square and triangular tessellation of the molecule taken as a unitary sphere, spherical tessellation of the molecular surface, numerical integration of the atomic volumes and surfaces, triangular tessellation of the molecular surface, and a cubic lattice approach to a molecular space. Accurate measures of the molecular volume and surface area have been performed with the pseudo-random Monte Carlo (MCVS) and uniform Monte Carlo (UMCVS) methods. These calculations serve as a reference for the…

On the Stochastic Response of a Fractionally-damped Duffing Oscillator

2012

A numerical method is presented to compute the response of a viscoelastic Duffing oscillator with fractional derivative damping, subjected to a stochastic input. The key idea involves an appropriate discretization of the fractional derivative, based on a preliminary change of variable, that allows to approximate the original system by an equivalent system with additional degrees of freedom, the number of which depends on the discretization of the fractional derivative. Unlike the original system that, due to the presence of the fractional derivative, is governed by non-ordinary differential equations, the equivalent system is governed by ordinary differential equations that can be readily h…

A numerical integration approach for fractional‐order viscoelastic analysis of hereditary‐aging structures

2019

Grafiska integrēšana un diferencēšana. Neperiodiskas līknes nolīdzinājuma atrašana

1931

Saturs: Funkcionāls sakars, tā attēlošana 3 Empirisks un racionāls nolīdzinājums 3 Pieskares konstrukcijas 6 Grafiska integrēšana 7 Grafiska diferencēšana 9 Līkņu veidi un nolīdzinājumi 10 Līkņu nolīdzinājumi pārveidotā koordinātu sistēmā 11 Deformācija 13 Līkņu pazīmes 13 Atsevišķi nolīdzinājumu veidi 17 Nolīdzinājuma atrašana, ja dots līknes zars 20 Piemēri 21 Nolīdzinājuma atrašana, kad doti līknes visi zari un īpaši punkti 25

An operator-like description of love affairs

2010

We adopt the so--called \emph{occupation number representation}, originally used in quantum mechanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relations. We start with a simple model, involving two actors (Alice and Bob): in the linear case we obtain periodic dynamics, whereas in the nonlinear regime either periodic or quasiperiodic solutions are found. Then we extend the model to a love triangle involving Alice, Bob and a third actress, Carla. Interesting features appear, and in particular we find analytical conditions for the linear model of love triangle to have periodic or quasiperiodic solutions. Numerical solutions are exhibi…