查看更多>>摘要：We propose a simple mathematical model to describe the evolution of violent crimes. For such purpose, we built a model based on ordinary differential equations that take into account the number of violent crimes and the number of legal and illegal guns. The dynamics is governed by probabilities, modeling for example the police action, the risk perception regarding crimes that leads to increase of ownership of legal guns, and so on. Our analytical and numerical results show that, in addition to the rise of criminality due to the presence of illegal guns, the increase of legal guns leads to a fast increase of violent crimes, suggesting that the access of firearms by civilians is not a good option regarding the control of crimes. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The global stabilization problem is investigated in the present paper for a class of stochastic nonlinear systems, whose structure is in a p-normal form (0 < p < 1) and states are perturbed by multiple time-varying delays. By means of an extended stability theory of stochastic nonlinear time-delay systems, where the existence and uniqueness of strong solution of an initial value problem is not required, a nonsmooth but continuous delay-dependent global stabilizer is systematically constructed to achieve the global strong asymptotic stability in probability of the closed-loop system under some conditions. In order to overcome the obstacles caused by low-order nonlinear terms, multiple time-varying delays and stochastic disturbances, a novel nonlinear Lyapunov-Krasovskii functional is skillfully introduced, which plays an important role in the controller design. The effectiveness of the obtained results is verified by an illustrative example in the end. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we introduce and analyze arbitrarily high-order quadrature rules for evaluating the two-dimensional singular integrals of the forms I-i,I-j = integral(R2) phi(x) x(i)x(j)/vertical bar x vertical bar(2+alpha) dx, 0 < alpha < 2 where i, j is an element of {1, 2} and phi is an element of C-c(N) for N >= 2. This type of singular integrals and its quadrature rule appear in the numerical discretization of fractional Laplacian in non-local Fokker-Planck Equations in 2D. The quadrature rules are trapezoidal rules equipped with correction weights for points around singularity. We prove the order of convergence is 2p + 4 - alpha, where p is an element of N-0 is associated with total number of correction weights. Although we work in 2D setting, we formulate definitions and theorems in n is an element of N dimensions when appropriate for the sake of generality. We present numerical experiments to validate the order of convergence of the proposed modified quadrature rules. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We propose for the first time some explicit closed-form Laguerre series expansion formulas for the first passage time density functions of a jump diffusion model. Suppose that the jumps in the model are phase-type distributed. In contrast to existing methods in the literature based on numerical Laplace transform inversion, the proposed formulas are in analytical closed-form and simple to implement. Two different methods are proposed to compute the Laguerre coefficients. Various numerical examples are also given to show the effectiveness of our method. (C) 2022 Published by Elsevier Inc.
Torres-Hernandez, A.Brambila-Paz, F.Montufar-Chaveznava, R.
16页
查看更多>>摘要：This paper presents one way to define an uncountable family of fractional fixed-point methods through a set of matrices that can generate a group of fractional matrix operators, as well as one way to define groups of fractional operators that are isomorphic to the group of integers under the addition, and shows one way to classify and accelerate the order of convergence of the family of proposed iterative methods, which may be useful to continue expanding the applications of the fractional operators. The proposed method to accelerate the order of convergence is used in a fractional iterative method, and with the obtained method are solved simultaneously two nonlinear algebraic systems that depend on time-dependent parameters, and that allow obtaining the temperatures and efficiencies of a hybrid solar receiver. Finally, two uncountable families of fractional fixed-point methods are presented, in which the proposed method to accelerate convergence can be implemented. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This manuscript deals with a novel hybrid spectral collocation approach to find the approximate solutions of a class of nonlinear partial differential equations of parabolic type pertaining to various important physical models in mathematical biology. The problem under consideration arises in the study of propagation of gene and transmission of nerve impulses. A second-order time discretization algorithm based on Taylor series expansion is first employed to tackle the underlying nonlinearity of the problem. Then, the spectral collocation approach based on the alternative Laguerre polynomials (with positive coefficients) is adopted for approximation of the resulting semi-discrete ordinary differential equations. The convergence of the spectral technique is established. Three numerical test examples are given to demonstrate the applicability and efficiency of the proposed approach. The computed results are compared with the results obtained by other available methods in order to show the advantage of our method. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper is devoted to present the rigorous unconditional stability and optimal error estimates of first order semi-implicit energy stable finite element method developed by Yang et al. (Comput. Methods Appl. Mech. Engrg. 356 (2019) 435-464) for the two phase magnetohydrodynamic(MHD) flows, some numerical results are also provided to show the performances of the considered numerical scheme. (C) 2022 Elsevier Inc. All rights reserved.
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