1,720,990 research outputs found
Relative error stability and instability of matrix exponential approximations for stiff numerical integration of long-time solutions
No full textWe study the relative error in the numerical integration of the long-time solution of a linear ordinary differential equation y′(t)=Ay(t),t≥0, where A is a normal matrix. The numerical long-time solution is obtained by using at any step an approximation of the matrix exponential. This paper analyzes the relative error in the stiff situation and it shows that, in this situation, some A-stable approximants exhibit instability with respect to perturbations in the initial value of the long-time solution
How perturbations in the matrix of linear systems of ordinary differential equations propagate along solutions
Full text linkThis paper addresses how perturbations in the matrix A propagate along the solution of the n-dimensional linear ordinary differential equation y′(t)=Ay(t),t≥0,y(0)=y0.In other words, for fixed t≥0 and y0∈Rn, we study the conditioning of the problem A↦etAy0.We also study the asymptotic behavior of the conditioning as t→+∞. The analysis is carried out for a normal matrix A
I servizi nei sindacati. Il caso dei Caf.
No full textIl primo capitolo analizza funzionalmente il ruolo dei servizi nei modelli alternativi di organizzazione sindacale, contestualizzando le riflessioni in una prospettiva storica. Il capitolo due introduce le attività in campo fiscale e di certificazione reddituale dei caf, ripercorrendo brevemente l’iter normativo. Il capitolo tre contiene un’analisi diacronica e territoriale dei soggetti che operano nel mercato delle dichiarazioni 730 e Ise. Nel capitolo quarto vengono indagate, mediante modelli di regressione ecologica, le relazioni tra la sindacalizzazione ed il mercato dei servizi fiscali. Il capitolo quinto sviluppa il tema del rapporto tra servizi e proselitismo associativo. Nel capitolo sesto sono analizzatii fattori determinanti la scelta di cambiare fornitore. Il capitolo settesviluppa delle ipotesi di strategie di marketing per i servizi erogati dal sindacato. Il capitolo conclusivo, sintetizzando l’intero percorso di ricerca, presenta alcune proposte operative
Time Reparametrization and Event Location for Discontinuous Differential Algebraic Equations
Full text linkIn this paper, we consider numerical methods for the event location of differential algebraic equations. The event corresponds to cross a discontinuity surface, beyond which another differential algebraic equation holds. The methods are based on a particular change of the independent variable time, called time reparametrization or time transformation, reducing the equation to another equation where the event time is known in advance. From a numerical point of view, these methods never cross the discontinuity surface and reach it in a fixed number of steps. The methods works also for differential algebraic equations of index higher than one
Time-transformations for the event location in discontinuous ODEs
Full text linkIn this paper, we consider numerical methods for the location of events of ordinary differential equations. These methods are based on particular changes of the independent variable, called time-transformations. Such a time-transformation reduces the integration of an equation up to the unknown point, where an event occurs, to the integration of another equation up to a known point. This known point corresponds to the unknown point by means of the time-transformation. This approach extends the one proposed by Dieci and Lopez [BIT 55 (2015), no. 4, 987-1003], but our generalization permits, amongst other things, to deal with situations where the solution approaches the event in a tangential way. Moreover, we also propose to use this approach in a different manner with respect to that of Dieci and Lopez
Preface to Stability of linear delay differential equations: A numerical approach with MATLAB
No full textNumerical approximation of characteristic values of partial retarded functional differential equations
No full textThe stability of an equilibrium point of a dynamical system is determined by the position in the complex plane of the so-called characteristic values of the line- arization around the equilibrium. This paper presents an approach for the computation of characteristic values of partial differential equations of evolution involving time delay, which is based on a pseudospectral method coupled with a spectral method. The convergence of the computed characteristic values is of infinite order with respect to the pseudospectral discretization and of finite order with respect to the spectral one. However, for one dimensional reaction diffusion equations, the finite order of the spectral discretization is proved to be so high that the convergence turns out to be as fast as one of infinite order
Efficient Computation of Stability Charts for Linear Time Delay Systems
No full textA new efficient algorithm for the computation of the stability chart of linear time delay systems is proposed and tested on several examples. The stability chart is obtained by investigating the 2d-parameter space by a first coarse square grid which is then adaptively refined by triangulation to match the desired tolerance. This leads to a considerable reduction in computational cost with respect to investigate a uniform fine square grid. Stability of each point is determined by approximating the rightmost characteristic root real part via a numerical scheme recently developed by the authors and based on pseudospectral differencing methods. A Matlab code is included in appendix
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