1,721,175 research outputs found
On the numerical structure preservation of nonlinear damped stochastic oscillators
Full text linkThe paper is focused on analyzing the conservation issues of stochastic-methods when applied to nonlinear damped stochastic oscillators. In particular, we are interested in reproducing the long-term properties of the continuous problem over its discretization through stochastic-methods, by preserving the correlation matrix. This evidence is equivalent to accurately maintaining the stationary density of the position and the velocity of a particle driven by a nonlinear deterministic forcing term and an additive noise as a stochastic forcing term. The provided analysis relies on a linearization of the nonlinear problem, whose effectiveness is proved theoretically and numerically confirmed
Long-term analysis of stochastic θ-methods for damped stochastic oscillators
No full textWe analyze long-term properties of stochastic θ-methods for damped linear stochastic oscillators. The presented a-priori analysis of the error in the correlation matrix allows to infer the long-time behaviour of stochastic θ-methods and their capability to reproduce the same long-term features of the continuous dynamics. The theoretical analysis is also supported by a selection of numerical experiments
Multivalue collocation methods free from order reduction
No full textThis paper introduces multivalue collocation methods for the numerical solution of stiff problems. The presented approach does not exhibit the phenomenon of order reduction, typical of collocation based Runge–Kutta methods applied to stiff systems, since the introduced methods have uniform effective order of convergence on the overall integration interval. Examples of methods as well as numerical experiments on a selection of stiff problems are given
Exponential mean-square stability properties of stochastic linear multistep methods
Full text linkThe aim of this paper is the analysis of exponential mean-square stability properties of nonlinear stochastic linear multistep methods. In particular it is known that, under certain hypothesis on the drift and diffusion terms of the equation, exponential mean-square contractivity is visible: the qualitative feature of the exact problem is here analysed under the numerical perspective, to understand whether a stochastic linear multistep method can provide an analogous behaviour and which restrictions on the employed stepsize should be imposed in order to reproduce the contractive behaviour. Numerical experiments confirming the theoretical analysis are also given
Nearly conservative multivalue methods with extended bounded parasitism
No full textThe paper is focused on the analysis of parasitism for multivalue numerical methods intended as geometric numerical integrators for Hamiltonian problems. In particular, the main topic is the design of multivalue numerical methods whose parasitic components remain bounded over certain time intervals, opening the path to the development of nearly conservative multivalue methods able to guarantee a control of parasitism in the long time. The analysis of parasitism as well as the development of the corresponding methods is the core of the treatise. The effectiveness of the approach is also confirmed on selected Hamiltonian problems
Epilepsy after head injury
No full textPURPOSE OF REVIEW: The purpose of this short review is to provide an update on the epidemiology of posttraumatic epilepsy, associated risk factors, data from prevention studies, and recent breakthroughs in experimental research.
RECENT FINDINGS: There is increasing evidence that neuroimaging findings, stratification by neurosurgical procedures performed, and genomic information (e.g. apolipoprotein E and haptoglobin genotypes) may provide useful predictors of the individual risk of developing posttraumatic epilepsy. While antiepileptic drug prophylaxis can be effective in protecting against acute (provoked) seizures occurring within 7 days after injury, no antiepileptic drug treatment has been found to protect against the development of posttraumatic epilepsy and therefore long-term anticonvulsant prophylaxis is not recommended. Glucocorticoid administration early after head injury also has not been found to reduce the risk of posttraumatic epilepsy. At the basic research level, there have been advances in the understanding of pathophysiological changes in posttraumatic excitatory and inhibitory synapses, and the critical period for epileptogenesis after head injury has been better defined. Finally, the development of a novel animal model, which mimicks more closely human posttraumatic epilepsy, may facilitate efforts to characterize relevant epileptogenic mechanisms and to identify clinically effective antiepileptogenic treatments.
SUMMARY: Despite the continuing lack of clinically effective agents for posttraumatic epilepsy prophylaxis, recent advances in basic and clinical research offer new hope for success in the development of new strategies for prevention and treatment
Filon quadrature for stochastic oscillators driven by time-varying forces
No full textIn this work, we propose a trigonometric stochastic numerical method for linear oscillators with high constant frequencies, driven by a nonlinear time-varying force and a random force. The scheme is obtained by applying the variation-of-constants formula and Filon quadrature, that is notoriously more effective for oscillating integrands. The development of the scheme and its analysis is equipped by numerical experiments on popular related physical models, confirming the effectiveness of the approach
Two-step Runge-Kutta methods for stochastic differential equations
No full textWe introduce a theory of two-step Runge-Kutta (TSRK) methods for stochastic differential equations, arising from the perturbation of the corresponding TSRK methods for deterministic problems. We present a proof of convergence and study the mean-square stability properties. Numerical experiments confirming the theoretical results are provided
Correction to: Exponential mean-square stability properties of stochastic linear multistep methods (Advances in Computational Mathematics, (2021), 47, 4, (55), 10.1007/s10444-021-09879-2)
No full textIn this article, the affiliation details for Raffaele D’Ambrosio was incorrectly given as “Department of Mathematics, University of Salerno, via Giovanni Paolo II, 132 - 84084, Fisciano (Sa), Italy” but should have been “Department of Information Engineering and Computer Science and Mathematics University of L'Aquila, Via Vetoio, Loc. Coppito,67100 L'Aquila“
Numerical conservation issues for the stochastic Korteweg–de Vries equation
No full textIn this paper, we focus on structure-preserving issues for the numerical solution of the stochastic Korteweg–de Vries equation, via stochastic θ-methods. It is well-known that the aforementioned model exhibits invariant laws along its exact dynamics. Here, our goal is to analyze whether such invariant laws are also reproduced along the numerical dynamics provided by stochastic θ-methods. Furthermore, we are also interested in rigorously studying the characterization of such invariant laws along numerical solutions of this model, with respect to the growth of the stochasticity parameter ɛ. At this purpose, the so-called ɛ-expansion of the exact solution to the aforementioned equation will be performed. Numerical results confirming the effectiveness of our analysis are also provided
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