CONSTRUCTIVE ASPECTS OF STABILITY RESEARCH IN SPECIAL CASES

2016 ◽  
Vol 8 (4) ◽  
pp. 18-26
Author(s):  
Котов ◽  
P. Kotov
Keyword(s):  
Differential Operator ◽  
Numerical Methods ◽  
Initial Conditions ◽  
Special Cases ◽  
Material Equation

The method of stability research of the dynamic status of system described by the material equation resolved concerning derivatives with the linear summary differential operator, limited elements of the initial conditions system and the substantial basis of numerical methods and of methods of basic researches is offered.

scholarly journals Analytical Study of the Difference Equation xn+1 = xnxn-6 / xn-5 (±1 – xnxn-6)

2019 ◽  
pp. 1-12
Author(s):  
Abdualrazaq Sanbo ◽  
Elsayed M. Elsayed ◽  
Faris Alzahrani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Analytical Study ◽  
Initial Conditions ◽  
Specific Form ◽  
Positive Real ◽  
Rational Difference Equations ◽  
Special Cases ◽  
The Difference

This paper is devoted to find the form of the solutions of a rational difference equations with arbitrary positive real initial conditions. Specific form of the solutions of two special cases of this equation are given.

scholarly journals Study of Second Hankel Determinant for Certain Subclasses of Functions Defined by Al-Oboudi Differential Operator

2020 ◽  
Vol 17 (1(Suppl.)) ◽  
pp. 0353
Author(s):  
K. A. Challab et al.
Keyword(s):  
Differential Operator ◽  
Upper Bound ◽  
Unit Disc ◽  
Hankel Determinant ◽  
Special Cases ◽  
Second Hankel Determinant

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

scholarly journals Numerical daemons of hydrological models are summoned by extreme precipitation

2021 ◽  
Author(s):  
Peter T. La Follette ◽  
Adriaan J. Teuling ◽  
Nans Addor ◽  
Martyn Clark ◽  
Koen Jansen ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Extreme Precipitation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Computational Cost ◽  
Numerical Error ◽  
Hydrological Models ◽  
Multiple Model ◽  
Numerical Techniques ◽  
Modeling Framework

Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on approximate numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation like that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation events. In this experiment, a large number of hydrographs is generated with the modular modeling framework FUSE, using eight numerical techniques across a variety of forcing datasets. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational expense and numerical error associated with each hydrograph were recorded. It was found that numerical error (root mean square error) usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both low numerical error and low computational cost. A basic literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be sub-optimal. We conclude that relatively large numerical errors might be common in current models, and because these will likely become larger as the climate changes, we advocate for the use of low cost, low error numerical methods.

scholarly journals A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems

2021 ◽  
Vol 8 (1) ◽  
pp. 1-11
Author(s):  
Abdul Abner Lugo Jiménez ◽  
Guelvis Enrique Mata Díaz ◽  
Bladismir Ruiz
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Initial Conditions ◽  
Stationary Regime ◽  
Heat Transfer Fluid ◽  
Mimetic Finite Difference Method ◽  
Linear Differential

Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since such problems present complex geometries, boundary or initial conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled with partial differential equations are diverse and these must be addressed numerically, so that the results obtained are more in line with reality. In this work, a comparison of the classical numerical methods such as: the finite difference method (FDM) and the finite element method (FEM), with a modern technique of discretization called the mimetic method (MIM), or mimetic finite difference method or compatible method, is approached. With this comparison we try to conclude about the efficiency, order of convergence of these methods. Our analysis is based on a model problem with a one-dimensional boundary value, that is, we will study convection-diffusion equations in a stationary regime, with different variations in the gradient, diffusive coefficient and convective velocity.

scholarly journals New Results on the Motions of Asteroids in Resonances

1992 ◽  
Vol 152 ◽  
pp. 145-152 ◽  
Author(s):  
R. Dvorak
Keyword(s):  
Initial Conditions ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Close Approach ◽  
Integration Time ◽  
Time Interval ◽  
Time Intervals ◽  
3 Dimensional ◽  
Special Cases ◽  
Good Agreement

In this article we present a numerical study of the motion of asteroids in the 2:1 and 3:1 resonance with Jupiter. We integrated the equations of motion of the elliptic restricted 3-body problem for a great number of initial conditions within this 2 resonances for a time interval of 104 periods and for special cases even longer (which corresponds in the the Sun-Jupiter system to time intervals up to 106 years). We present our results in the form of 3-dimensional diagrams (initial a versus initial e, and in the z-axes the highest value of the eccentricity during the whole integration time). In the 3:1 resonance an eccentricity higher than 0.3 can lead to a close approach to Mars and hence to an escape from the resonance. Asteroids in the 2:1 resonance with Jupiter with eccentricities higher than 0.5 suffer from possible close approaches to Jupiter itself and then again this leads in general to an escape from the resonance. In both resonances we found possible regions of escape (chaotic regions), but only for initial eccentricities e > 0.15. The comparison with recent results show quite a good agreement for the structure of the 3:1 resonance. For motions in the 2:1 resonance our numeric results are in contradiction to others: high eccentric orbits are also found which may lead to escapes and consequently to a depletion of this resonant regions.

scholarly journals CONFORMAL DERIVATIVE AND CONFORMAL TRANSPORTS OVER $\bm{({\bar L}_n,g)}$-SPACES

2000 ◽  
Vol 15 (05) ◽  
pp. 679-695 ◽  
Author(s):  
S. MANOFF
Keyword(s):  
Vector Field ◽  
Differential Operator ◽  
Harmonic Oscillator ◽  
Vector Fields ◽  
Gravitational Theory ◽  
Orthogonal Vector ◽  
Special Cases

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as "conformal" transports and investigated over [Formula: see text]-spaces. They are more general than the Fermi–Walker transports. In an analogous way as in the case of Fermi–Walker transports a conformal covariant differential operator and its conformal derivative are defined and considered over [Formula: see text]-spaces. Different special types of conformal transports are determined inducing also Fermi–Walker transports for orthogonal vector fields as special cases. Conditions under which the length of a non-null contravariant vector field could swing as a homogeneous harmonic oscillator are established. The results obtained regardless of any concrete field (gravitational) theory could have direct applications in such types of theories.

On Growth-Collapse Processes with Stationary Structure and Their Shot-Noise Counterparts

2009 ◽  
Vol 46 (02) ◽  
pp. 363-371 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Growth Process ◽  
Initial Conditions ◽  
Steady State Distribution ◽  
State Distribution ◽  
Stationary Structure ◽  
Stationary Version ◽  
Special Cases ◽  
The Times

In this paper we generalize existing results for the steady-state distribution of growth-collapse processes. We begin with a stationary setup with some relatively general growth process and observe that, under certain expected conditions, point- and time-stationary versions of the processes exist as well as a limiting distribution for these processes which is independent of initial conditions and necessarily has the marginal distribution of the stationary version. We then specialize to the cases where an independent and identically distributed (i.i.d.) structure holds and where the growth process is a nondecreasing Lévy process, and in particular linear, and the times between collapses form an i.i.d. sequence. Known results can be seen as special cases, for example, when the inter-collapse times form a Poisson process or when the collapse ratio is deterministic. Finally, we comment on the relation between these processes and shot-noise type processes, and observe that, under certain conditions, the steady-state distribution of one may be directly inferred from the other.

Dynamic Analysis of a Viscoelastic Nanobeam

2019 ◽  
Vol 799 ◽  
pp. 223-229 ◽  
Author(s):  
Mustafa Arda ◽  
Metin Aydogdu
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Initial Conditions ◽  
Nonlocal Elasticity Theory ◽  
Equation Of Motion ◽  
Critical Buckling Load ◽  
Damping Effect ◽  
Material Equation

Vibration of an axially loaded viscoelastic nanobeam is analyzed in this study. Viscoelasticity of the nanobeam is modeled as a Kelvin-Voigt material. Equation of motion and boundary conditions for viscoelastic nanobeam are provided with help of Eringen’s Nonlocal Elasticity Theory. Initial conditions are used in solution of governing equation of motion. Damping effect of the viscoelastic nanobeam structure is investigated. Nonlocal effect on natural frequency and damping of nanobeam and critical buckling load is obtained.

Exact solutions for scalar field cosmology in f(R) gravity

2017 ◽  
Vol 32 (30) ◽  
pp. 1750164 ◽  
Author(s):  
S. D. Maharaj ◽  
R. Goswami ◽  
S. V. Chervon ◽  
A. V. Nikolaev
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Scalar Curvature ◽  
Evolution Equations ◽  
Initial Conditions ◽  
De Sitter ◽  
Airy Functions ◽  
Special Cases ◽  
The Universe ◽  
Current Stage

We study scalar field FLRW cosmology in the content of f(R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f(R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f(R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f(R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the [Formula: see text]CDM model.

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