discretization step
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2022 ◽  
pp. 133-155
Author(s):  
Giulio Ferro ◽  
Riccardo Minciardi ◽  
Luca Parodi ◽  
Michela Robba

The relevance of electric vehicles (EVs) is increasing along with the relative issues. The definition of smart policies for scheduling the EVs charging process represents one of the most important problems. A discrete-event approach is proposed for the optimal scheduling of EVs in microgrids. This choice is due to the necessity of limiting the number of the decision variables, which rapidly grows when a small-time discretization step is chosen. The considered optimization problem regards the charging of a series of vehicles in a microgrid characterized by renewable energy source, a storage element, the connection to the main grid, and a charging station. The objective function to be minimized results from the weighted sum of the cost for purchasing energy from the external grid, the weighted tardiness of the services provided, and a cost related to the occupancy of the socket. The approach is tested on a real case study.


Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 125
Author(s):  
Vigirdas Mackevičius ◽  
Gabrielė Mongirdaitė

In this paper, we construct first- and second-order weak split-step approximations for the solutions of the Wright–Fisher equation. The discretization schemes use the generation of, respectively, two- and three-valued random variables at each discretization step. The accuracy of constructed approximations is illustrated by several simulation examples.


Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1337
Author(s):  
Gytenis Lileika ◽  
Vigirdas Mackevičius

In this paper, we construct second-order weak split-step approximations of the CKLS and CEV processes that use generation of a three−valued random variable at each discretization step without switching to another scheme near zero, unlike other known schemes (Alfonsi, 2010; Mackevičius, 2011). To the best of our knowledge, no second-order weak approximations for the CKLS processes were constructed before. The accuracy of constructed approximations is illustrated by several simulation examples with comparison with schemes of Alfonsi in the particular case of the CIR process and our first-order approximations of the CKLS processes (Lileika– Mackevičius, 2020).


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mikhail M. Kokurin

Abstract Finite difference semidiscretization methods for solving an ill-posed Cauchy problem in a Hilbert space are investigated. The problems involve linear positively definite selfadjoint operators. We justify an a posteriori scheme for the choice of the time-discretization step and establish accuracy estimates in terms of the error level of input data.


Author(s):  
Giulio Ferro ◽  
Riccardo Minciardi ◽  
Luca Parodi ◽  
Michela Robba

AbstractThe relevance and presence of Electric Vehicles (EVs) are increasing all over the world since they seem an effective way to fight pollution and greenhouse gas emissions, especially in urban areas. One of the main issues related to EVs is the necessity of modifying the existing infrastructure to allow the installation of new charging stations (CSs). In this scenario, one of the most important problems is the definition of smart policies for the sequencing and scheduling of the vehicle charging process. The presence of intermittent energy sources and variable execution times represent just a few of the specific features concerning vehicle charging systems. Even though optimization problems regarding energy systems are usually considered within a discrete time setting, in this paper a discrete event approach is proposed. The fundamental reason for this choice is the necessity of limiting the number of the decision variables, which grows beyond reasonable values when a short time discretization step is chosen. The considered optimization problem regards the charging of a series of vehicles by a CS connected with a renewable energy source, a storage element, and the main grid. The objective function to be minimized results from the weighted sum of the (net) cost for purchasing energy from the external grid, the weighted tardiness of the services provided to the customers, and a cost related to the occupancy of the socket during the charging. The approach is tested on a real case study. The limited computational burden allows also the implementation in real-case applications.


2020 ◽  
Vol 12 (6) ◽  
pp. 50
Author(s):  
Christian Vanhille

We propose an iterative method to evaluate the roots of nonlinear equations. This Secant-based technique approximates the derivatives of the function numerically through a constant discretization step h disassociated from the iterative progression. The algorithm is developed, implemented, and tested. Its order of convergence is found to be h-dependent. The results obtained corroborate the theoretical deductions and evidence its excellent behavior. For infinitesimal h-values, the algorithm accelerates the convergence of the Secant method to order 2 (the one of the Newton-Raphson method) with no need for analytic expression of derivatives (the advantage of the Secant method).


Author(s):  
Vito Crismale ◽  
Giovanni Scilla ◽  
Francesco Solombrino

AbstractWe analyze a finite-difference approximation of a functional of Ambrosio–Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step $$\delta $$ δ is smaller than the ellipticity parameter $$\varepsilon $$ ε , we show the $$\varGamma $$ Γ -convergence of the model to the Griffith functional, containing only a term enforcing Dirichlet boundary conditions and no $$L^p$$ L p fidelity term. Restricting to two dimensions, we also address the case in which a (linearized) constraint of non-interpenetration of matter is added in the limit functional, in the spirit of a recent work by Chambolle, Conti and Francfort.


Author(s):  
G Deugoué ◽  
B Jidjou Moghomye ◽  
T Tachim Medjo

Abstract In this paper we study the numerical approximation of the stochastic Cahn–Hilliard–Navier–Stokes system on a bounded polygonal domain of $\mathbb{R}^{d}$, $d=2,3$. We propose and analyze an algorithm based on the finite element method and a semiimplicit Euler scheme in time for a fully discretization. We prove that the proposed numerical scheme satisfies the discrete mass conservative law, has finite energies and constructs a weak martingale solution of the stochastic Cahn–Hilliard–Navier–Stokes system when the discretization step (both in time and in space) tends to zero.


2020 ◽  
Vol 10 (12) ◽  
pp. 4263 ◽  
Author(s):  
Xin Liu ◽  
Tianping Ge

In the implementation of the Cooray–Rubinstein formula, the calculation of a lightning electromagnetic field over perfectly conducting ground accounted for most of the computation time. Commonly, evaluating the ideal lightning electromagnetic field is based on the numerical integration method. In practice, only a sufficiently small discretization step is essential to get an accurate result, which leads to a relatively large number of calculations and results in a lengthy computation time. Besides, the programming is relatively complicated because the propagation of the lightning current along the channel must be considered. In order to increase the efficiency and simplify the programming, an improved method is proposed in this paper. In this method, the evaluation of the ideal lightning electromagnetic field is equated with a summation of analytical formulae and a simple integral operation, so it would be more efficient and easily programmed. The validation of the proposed method is demonstrated by some simulation examples.


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