Computational and Mathematical Methods最新文献

Current Internet of Things (IoT) scenarios have to deal with many challenges especially when a large amount of heterogeneous data sources are integrated, that is, data curation. In this respect, the use of poor-quality data (i.e., data with problems) can produce terrible consequence from incorrect decision-making to damaging the performance in the operations. Therefore, using data with an acceptable level of usability has become essential to achieve success. In this article, we propose an IoT-big data pipeline architecture that enables data acquisition and data curation in any IoT context. We have customized the pipeline by including the DMN4DQ approach to enable us the measuring and evaluating data quality in the data produced by IoT sensors. Further, we have chosen a real dataset from sensors in an agricultural IoT context and we have defined a decision model to enable us the automatic measuring and assessing of the data quality with regard to the usability of the data in the context.

The problem of computing periodic solutions can be expressed as a boundary value problem and solved numerically via piecewise collocation. Here, we extend to renewal equations the corresponding method for retarded functional differential equations in (K. Engelborghs et al., SIAM J Sci Comput., 22 (2001), pp. 1593–1609). The theoretical proof of the convergence of the method has been recently provided in (A. Andò and D. Breda, SIAM J Numer Anal., 58 (2020), pp. 3010–3039) for retarded functional differential equations and in (A. Andò and D. Breda, submitted in 2021) for renewal equations and consists in both cases in applying the abstract framework in (S. Maset, Numer Math., 133 (2016), pp. 525–555) to a reformulation of the boundary value problem featuring an infinite-dimensional boundary condition. We show that, in the renewal case, the proof can also be carried out and even simplified when considering the standard formulation, defined by boundary conditions of finite dimension.

In this work, we have proposed a numerical approach for solving the incompressible Navier–Stokes equations in the streamfunction-vorticity formulation. The numerical scheme is based on the diagonally implicit fractional-step $��\theta �-�$(DIFST) method used for the time discretization and the conforming finite element method for the spatial discretization. The accuracy and efficiency of the scheme are validated by solving some benchmark problems. The numerical simulations are carried out using the DUNE-PDELab open-source software package. The comparison of DIFST scheme with different time discretization schemes is provided in terms of CPU time. Also, different solvers with preconditioners are investigated for solving the resulting algebraic system of equations numerically.

In this article, a new technique is used to solve the nonlinear boundary value problem of a cantilever-type nanoelectromechanical system. The technique is called the optimal perturbation iteration method and it is used to solve the problem in the form of a nonlinear differential equation with negative power-law nonlinearity. A convergence and error estimation of the proposed method is presented proving that the method is convergent. Results for the application of the proposed technique are demonstrated through two examples and the tables and figures prove that the method is efficient and straightforward.

An efficient modification of the Chebyshev method is constructed from approximating the second derivative of the operator involved by combinations of the operator in different points and it is used to locate, separate, and approximate the solutions of a Chandrasekhar integral equation from analysing its global convergence.

In this article, we propose a new research related to the convergence of the frozen Potra and Schmidt–Schwetlick schemes when we apply to equations. The purpose of this study is to introduce a comparison between two solutions to equations under the same conditions. In particular, we show the convergence radius and the uniqueness ball coincidence, while the error estimates are generally different. In this work, we extended the local convergence for Banach space valued operators using only the divided difference of order one and the first derivative of the schemes. This is a great advantage since we improve convergence by avoiding calculating higher-order derivatives that can either be difficult or not even exist. On the other hand, we also present a dynamical study of the behavior of a method compared with its no frozen alternative in order to see the behavior of both. We will study the basins of attraction of the two methods to three different polynomials involving two real, three real, and two real and two complex different solutions.

This article investigates a prey–predator model incorporating a novel refuge proportional to prey and inverse proportion to the predator. We find conditions for the local asymptotic stability of fixed points of the proposed prey–predator model. This article presents Neimark–Sacker bifurcation (NSB) and period-doubling bifurcation (PDB) at particular parameter values for positive equilibrium points of the proposed refuge-based prey–predator system. The system exhibits the chaotic dynamics at increasing values of the bifurcation parameter. The hybrid control methodology will control the chaos of the proposed prey–predator dynamical system and discuss the chaotic situation for different biological parameters through graphical analysis. Numerical simulations support the theoretical outcome and long-term chaotic behavior over a broad range of parameters.

The aim of this article is to study the local convergence of a generalized $��m�+�2�$-step solver with nondecreasing order of convergence $��3�m�+�3�$. Sharma and Kumar gave the order of convergence using Taylor series expansions and derivatives up to the order $��3�m�+�4�$ that do not appear in the method. Hence, the applicability of it is very limited. The novelty of our article is that we use only the first derivative in our local convergence (that only appears on the proposed method). Error bounds and uniqueness results not given earlier are also provided based on q-continuity functions. We also work with Banach space instead of Euclidean space valued operators. This way the applicability of the solver is extended. Applications where the convergence criteria are tested to complete this article.

This article deals with mathematical modeling and simulation of heat transfer in tissue under periodic boundary condition using nonlinear dual-phase-lag-bioheat-transfer (DPLBHT). We have taken the temperature dependent blood perfusion and metabolic heat source as exponent variation in nonlinear DPLBHT model, both are experimentally validated function of temperature. In this article we applied finite difference method and Runge–Kutta (4,5) scheme to solve nonlinear problem. In particular case the exact solution is obtained and compared with numerical scheme and both are in good agreement. Effect of different parameters are discussed in detail such as blood perfusion rate, dimensionless heat source parameters, relaxation, and thermalization time on dimensionless temperature. The whole article is analyzed in dimensionless form.

Bonelli's eagle (Hieraaetus fasciatus), a threatened species in Western Europe, has suffered a critical and severe decline in last two decades. In this article, a qualitative analysis of an ecoepidemiological model which consists of two prey and a predator is carried out. We proposed and designed a spatiotemporal model to predict the distribution of a territorial predator, Bonelli's eagle and its two main prey species (rabbit and red-legged partridge). Bounded positive solution, feasibility of the equilibria, and their stability analysis are determined for the nonspatial counterpart of the system. Criteria for diffusion-driven instability caused by local random movements of rabbits, partridges, and Bonelli's eagle are obtained. Possible implications of the result for Bonelli's eagle conservation are discussed. We show that the inclusion of second prey in the system can drastically change the dynamics from the single prey case. We also found that the presence of a second prey is beneficial for the conservation of the threatened Bonelli's eagle population in Europe. Results obtained from theoretical analysis of the nonspatial model agree very well with the numerical simulation results. Lastly, via numerical simulation, we illustrate the effect of diffusion of the dynamical system in the spatial/spatiotemporal domain by different pattern formations.