Search results for "Numerical Analysis"
showing 10 items of 883 documents
A New Look at the Stochastic Linearization Technique for Hyperbolic Tangent Oscillator
1998
Abstract Stochastic linearization technique is reconsidered for oscillator with restoring force in form of hyperbolic tangent. We show that a subtle error was made in the previously known procedure for derivation of the linearized system parameters. Two new error-free procedures, namely, those based on minimization of mean square difference between (a) restoring force or (b) potential energy of the original non-linear system and their linear counterparts, are suggested. The results of numerical analysis are shown.
Some Improvements on Relativistic Positioning Systems
2018
[EN] We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropr…
Typhetum laxmannii (Ubrizsy 1961) Nedelcu 1968 - The new plant association in Poland
2011
<em>Typhetum laxmannii</em> (Ubrizsy 1961) Nedelcu 1968 is a plant association new to Poland, built by an expansive kenophyte - <em>Typha laxmannii</em> Lepech. This paper presents the general distribution of both, the species and the association, paying particular attention to the area of Europe and Poland where, in recent years, many new locations as well as an increasing participation in vegetation cover have been observed. The habitat preferences of <em>Typhetum laxmannii</em>, the floristic composition of the association and its geographical differentiation within the occupied area are described. The current distribution of the association in Poland …
NUMERICAL ALGORITHMS
2013
For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a …
Explicit closed form solutions of boundary value problems for systems of difference equations
1990
In this paper boundary value problems for systems of difference equations of the type , where A j ∈ C p×p and bn y j+n ∈ C p , for 0≤j≤k − 1, are studied from an algebraic point of view. Existence conditions and closed form solutions are given in terms of co-solutions of the algebraic matrix equation .
Exact simulation of first exit times for one-dimensional diffusion processes
2019
International audience; The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study …
Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics
2018
We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into General Relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows to generate solutions of the former from those of the latter using purely algebraic transformations. This correspondence is explicitly illustrated with the Eddington-inspired Born-Infeld theory of gravity, for which we consider a family of nonlinear electrodynamics and show that, under the map, preserve their algebraic structure. For the particular case of Maxwell electrodynamics coupled to Born-Infeld gravity we find, via this corresponden…
Periodic Discrete Splines
2014
Periodic discrete splines with different periods and spans were introduced in Sect. 3.4. In this chapter, we discuss families of periodic discrete splines, whose periods and spans are powers of 2. As in the polynomial splines case, the Zak transform is extensively employed. It results in the Discrete Spline Harmonic Analysis (DSHA). Utilization of the Fast Fourier transform (FFT) enables us to implement all the computations in a fast explicit way.
A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains
2014
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains (Ciraolo et al. in J Comput Phys 246:78–95, 2013) where the index of refraction is not required to be constant at infinity. The approach is based on the minimization of an integral functional, which arises from an integral formulation of the radiation condition at infinity. In this paper, we implement a Fourier–Chebyshev collocation method to study some convergence properties of the numerical algorithm; in particular, we give numerical evidence of some convergence estimates available in the literature (Ciraolo in Helmholtz equation in unbou…
Monotonicity and local uniqueness for the Helmholtz equation
2017
This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local…