Search results for "Numerical Analysis"
showing 10 items of 883 documents
bssm: Bayesian Inference of Non-linear and Non-Gaussian State Space Models in R
2021
We present an R package bssm for Bayesian non-linear/non-Gaussian state space modelling. Unlike the existing packages, bssm allows for easy-to-use approximate inference based on Gaussian approximations such as the Laplace approximation and the extended Kalman filter. The package accommodates also discretely observed latent diffusion processes. The inference is based on fully automatic, adaptive Markov chain Monte Carlo (MCMC) on the hyperparameters, with optional importance sampling post-correction to eliminate any approximation bias. The package implements also a direct pseudo-marginal MCMC and a delayed acceptance pseudo-marginal MCMC using intermediate approximations. The package offers …
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
A finite-difference method for numerical solution of the steady-state nernst—planck equations with non-zero convection and electric current density
1986
Abstract A computer algorithm has been developed for digital simulation of ionic transport through membranes obeying the Nernst—Planck and Poisson equations. The method of computation is quite general and allows the treatment of steady-state electrodiffusion equations for multiionic environments, the ionic species having arbitrary valences and mobilities, when convection and electric current are involved. The procedure provides a great flexibility in the choice of suitable boundary conditions and avoids numerical instabilities which are so frequent in numerical methods. Numerical results for concentration and electric potential gradient profiles are presented in the particular case of the t…
A validated energy model of a solar dish-Stirling system considering the cleanliness of mirrors
2020
Solar systems based on the coupling of parabolic concentrating collectors and thermal engines (i.e. dish-Stirling systems) are among the most efficient generators of solar power currently available. This study focuses on the modelling of functioning data from a 32 kWe dish-Stirling solar plant installed at a facility test site on the University of Palermo campus, in Southern Italy. The proposed model, based on real monitored data, the energy balance of the collector and the partial load efficiency of the Stirling engine, can be used easily to simulate the annual energy production of such systems, making use of the solar radiation database, with the aim of encouraging a greater commercialisa…
A subtle error in conventional stochastic linearization techniques
1998
Abstract The stochastic linearization technique as applied to the SDOF system is re-examined. Two standard procedures associated with the stochastic linearization, widely adopted in the literature, are shown to be erroneous. Two new procedures to correct the errors made in previous works are introduced. To gain more insight, the procedures are applied to the quintic oscillator. Comparative numerical analysis is performed.
Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses
1997
Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.
Linear Systems Excited by Polynomials of Filtered Poission Pulses
1997
The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been derived. It is shown that the moment equations constitute a linear finite set of differential equatio…
WENO schemes applied to the quasi-relativistic Vlasov-Maxwell model for laser-plasma interaction
2014
Abstract In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov–Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge–Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.
Boundary Integral Formulation for Composite Laminates in Torsion
1997
The three-dimensional elastic stress state in a general composite laminate under twisting load is given. The analysis is carried out through an integral equation formulation that is numerically solved by the boundary element method. The integral representation of the elastic behavior is deduced by means of the reciprocity theorem applied to the actual response of each ply and the problem's analytical singular fundamental solutions. The interface continuity conditions due to perfect bonding are considered to complete the laminate mathematical model. The method permits the analysis for generally stacked laminates having general shape of the cross section. By virtue of the formulation characte…
INVESTIGATIONS OF STRAIN AND STRESS STATE AND CAPACITY IN SHORT CYLINDRICAL SHELLS UNDER INTERNAL PRESSURE
1989
In the paper it has been assumed that a triaxial stress and strain state occurs in a shell. The finite element method was used and owing to that digitization of the problem was possible. Such digitization was necessary for a numerical analysis of the moment stress state in the shell. On the ground of physical relations of the Prandtl-Reuss plastic flow theory an algorithm was formulated. The algorithm was a basis of calculating strains and stresses and determining capacity in a short cylindrical shell with rigid bottoms. The shell was subject to internal pressure. Experiments were carried out, as well. The results obtained with: equations of the membraneous shell theory, using plastic flow …