Computational and Mathematical Methods最新文献

An outbreak of severe acute respiratory syndrome (COVID-19) killed 287,355 with 4, 257,578 cases worldwide as of May 12, 2020. In this paper, we propose an SEQI_sI_aRM deterministic mathematical model which contains compartments for both human-to-human transmission and transmission through contaminated surfaces. Without intervention, the role of symptomatic and asymptomatic cases in humans is found to be very high in the transmission of the virus. Sensitive parameters which are associated with increased transmission of the COVID-19 virus were identified. According to the sensitivity results, the most sensitive parameters were disease-induced death rates of symptomatic and asymptomatic infectious people (σ), the rate of removal of virus from surfaces and environment (ν), and the rate of infection by asymptomatic infectious people (λ₂) and symptomatic infectious people (λ₁). The numerical results of our model confirm the sensitivity results that there are more new incidences of asymptomatic cases than symptomatic cases, which escalates the transmission of the virus in the community. Combined interventions like increasing both the rate of removal of viruses from surfaces and environment and decreasing the rate of infection in asymptomatic cases can play a significant role in reducing the average number of secondary infection (R₀) to less than unity, causing COVID-19 to die out.

An N-dimensional game theory–based model for multi-actor predictive analytics is presented in this article. The proposed model expands our previous work on two-dimensional group decision model for predictive analytics. The one-dimensional models are used for the problems where actors are interacting in a single issue space only. This is less than an ideal assumption since; in most cases, players’ strategies may depend on the dynamics of multiple issues when dealing with other players. In this work, the one-dimensional model is expanded to N-dimensional model by considering different positions, and separate salience values, across different axes for the players. The model predicts an outcome for a given problem by taking into account stakeholder’s positions in different dimensions and their conflicting perspectives. To illustrate the capability of the proposed model, three case studies have been presented.

There has been several Lagrange and Hermite type interpolations of entire functions whose linear canonical transforms have compact supports in ℝ. There interpolation representations are called sampling theorems for band-limited signals in signal analysis. The truncation, amplitude, and jitter errors associated with the Lagrange type interpolations are investigated rigorously. Nevertheless, the amplitude and jitter errors arising from perturbing samples and nodes are not studied before. The aim of this work is to establish rigorous analysis of their types of perturbation errors, which is important from both practical and theoretical points of view. We derive precise estimates for both types of errors and expose various numerical examples.

This paper mainly deals on the issue of a chaotic synchronization of a master and slave systems. It is generally the requirement of the synchronization that someone needs at least one to one master and slave systems. In the current study, the authors introduce the concept of a synchronization in which there is no need of slave/response system externally. Furthermore, the synchronization has been demonstrated here within a system among the subsystems of different orders. In addition, adaptive control is chosen for the synchronization among various combinations in multiswitching manner. For demonstration purpose, Lorenz Six Dimensional Hyper Chaotic System (L6DHCS) is chosen. There are three different kinds of possible switches presented by the authors formed within the considered system. The numerical simulations are carried out to validate the effectiveness of the analytical technique using Mathematica.

In this paper, we present a new computational method based on an exponential spline for solving a class of delay differential equations with a negative shift in the differentiated term. When the shift parameter is O(ε), the proposed method works well and also controls the oscillations in the solution’s layer region. To accomplish this, we included a parameter in the proposed numerical scheme that is based on a special type of mesh, and the parameter is evaluated using the theory of singular perturbation. Maximum absolute errors and convergences of numerical solutions are tabulated to demonstrate the efficiency of the proposed computational method and to support the convergence analysis of the presented scheme.

This article suggests two new modified iteration methods called the modified Gauss-Seidel (MGS) method and the modified fixed point (MFP) method to solve the absolute value equation. Using appropriate assumptions, we examine the convergence of the given methods. Lastly, numerical examples illustrate the usefulness of the new strategies.

The time-dependent neutron diffusion equation approximates the neutronic power evolution inside a nuclear reactor core. Applying a Galerkin finite element method for the spatial discretization of these equations leads to a stiff semi-discrete system of ordinary differential equations. For time discretization, an implicit scheme is used, which implies solving a large and sparse linear system of equations for each time step. The GMRES method is used to solve these systems because of its fast convergence when a suitable preconditioner is provided. This work explores several matrix-free strategies based on different updated preconditioners, which are constructed by low-rank updates of a given initial preconditioner. They are two tuned preconditioners based on the bad and good Broyden’s methods, initially developed for nonlinear equations and optimization problems, and spectral preconditioners. The efficiency of the resulting preconditioners under study is closely related to the selection of the subspace used to construct the update. Our numerical results show the effectiveness of these methodologies in terms of CPU time and storage for different nuclear benchmark transients, even if the initial preconditioner is not good enough.

Due to the specificity of the Weibull tail coefficient, most of the estimators available in the literature are based on the log excesses and are consequently quite similar to the estimators used for the estimation of a positive extreme value index. The interesting performance of estimators based on generalized means leads us to base the estimation of the Weibull tail coefficient on the power mean-of-order-p. Consistency and asymptotic normality of the estimators under study are put forward. Their performance for finite samples is illustrated through a Monte Carlo simulation. It is always possible to find a negative value of p (contrarily to what happens with the mean-of-order-p estimator for the extreme value index), such that, for adequate values of the threshold, there is a reduction in both bias and root mean square error.

We propose a discrete data classification method of scattered data in N-dimensional by solving the minimax problem for a set of points. The current research is extended from 2-dimensional and 3-dimensional to N-dimensional. The problem can be applied to artificial intelligence classification problems (machine learning, deep learning), point data analysis problems (data science problem), the optimized design of nanoscale circuits, and the location of facility problems, circle detection on 2D image, or sphere detection on depth image. We generalized the discrete data classification methodology in N-dimensional. Finally, we resolved to find an exact solution of the location of a manifold for our suggested problem in N-dimensional.

In this paper, we provide two new generalized Gauss-Seidel (NGGS) iteration methods for solving absolute value equations Ax − ∣x | = b, where A ∈ R^n×n, b ∈ Rⁿ, and x ∈ Rⁿ are unknown solution vectors. Also, convergence results are established under mild assumptions. Eventually, numerical results prove the credibility of our approaches.