查看更多>>摘要：This paper develops a numerical two-level explicit approach for solving a mathematical model for the spread of Covid-19 pandemic with that includes the undetected infectious cases. The stability and convergence rate of the new numerical method are deeply analyzed in the L-infinity-norm. The proposed technique is less time consuming than a broad range of related numerical schemes. Furthermore, the method is stable, and at least second-order accurate and it can serve as a robust tool for the integration of general ODEs systems of initial-value problems. Some numerical experiments are provided which include the pandemic in Cameroon, and discussed. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper deals with the strong convergence and exponential stability of the stochastic theta (ST) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs) with non-Lipschitzian and non-linear coefficients and mainly includes the following three results: (i) under the local Lipschitz and the monotone conditions, the ST method with theta is an element of [1/2, 1] is strongly convergent to SDEPCAs; (ii) the ST method with theta is an element of (1/2, 1] preserves the exponential mean square stability of SDEPCAs under the monotone condition and some conditions on the step-size; (iii) without any restriction on the step-size, there exists theta* is an element of (1/2, 1] such that the ST method with theta is an element of (theta*, 1] is exponentially stable in mean square. Moreover, for sufficiently small step-size, the rate constant can be reproduced. Some numerical simulations are provided to illustrate the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Domain Decomposition Methods are a set of strategies to realize simulations splitting the whole domain into smaller parts, analyzing each one of them separately on dif-ferent processors and exchanging information between subdomains. The mixed domain decomposition approach depends on a specific parameter called search direction, which allows communicating subdomains. Previously studies suggest some approximations for this sensitive parameter, but in the great majority, only the short-range contributions are taken into account. In the present work, a new expression for the search direction called two-scale impedance is implemented in 3 different simple structures composed of beams, which present local buckling and post-buckling, generating geometrical nonlinearities on their behaviors. The aim is to test the efficiency of this new expression in structures with this kind of nonlinearities, catching the advantages and disadvantages that the use of the two-scale impedance may lead, all this in order to project its real applicability at an industrial level. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the present paper, the continuous form of the higher degree Fuzzy transform (Fm -transform) technique is used for the numerical solution of the second kind Volterra integral equations with singular and nonsingular kernels. By employing this method, the equation is converted to the system of linear algebraic equations with a lower Hessenberg coefficient matrix. It is shown that the coefficient matrix is invertible. The error analysis is carried out for the solution procedure. The results show that for singular kernels, the accuracy decreases with an increasing degree of fuzzy transform due to the non-differentiability of the kernel. Experiments on nonsingular kernels show convergence with an increasing degree of fuzzy transform. As expected, the accuracy of the method improves with partition numbers for both singular and nonsingular kernels. Some examples are given to illustrate the theoretical results. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：As a widely used model, Mixture Density Model (MDM) is traditionally solved by Expectation-Maximization (EM) algorithm. EM maximizes a lower bound function iteratively, especially for exponential families. This paper managed to improve EM by combining it with Total Least Squares (TLS), proposing a new algorithm called the TLS-EM algorithm. In this algorithm, parameters are divided into two groups, linear parameters and sub-model parameters. They are solved in each iteration separately. First, data set is separated in different intervals and the conditional maximizing question is transformed into the over-determined linear equations. TLS is adopted to solve these equations and calculate linear parameters, with sub-model parameters fixed. Second, sub-model parameters are solved with EM. Properties of TLS-EM have been provided with proofs. Combining the properties of TLS, EM and the properties of its own, TLS-EM not only inherits most advantages of EM but also improves it in most cases, especially in bad initial or bad model conditions. Numerical experiments confirm these properties. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we aim to develop a highly efficient numerical scheme for the flow-coupled phase-field model of diblock copolymer melt. Formally, the model is a very complicated nonlinear system that consists of the Navier-Stokes equations and the Cahn-Hilliard type equations with the Ohta-Kawaski potential. Through a combination of a novel decoupling technique and the projection method, we develop the first full decoupling, energy stable, and second-order time-accurate numerical scheme for this model. The decoupling technique is based on the design of an auxiliary ODE, which plays a vital role in obtaining the full decoupling structure while maintaining energy stability. The high efficiency of the scheme is not only reflected by its linear and decoupled structure but also because it only needs to solve a few elliptic equations at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Numerical experiments further verify the convergence rate, energy stability, and effectiveness of the developed algorithm. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, a detailed theoretical and experimental study on some computational aspects of high order discrete orthogonal Racah polynomials (RPs) and their corresponding moments is carried out. Initially, the numerical overflow problem related to RPs computation is solved by using modified recurrence relations of RPs with respect to the polynomial order n and the variable s. Moreover, the recursive nature of the resulting relations considerably accelerates the computation of RPs. Then, the problem of numerical errors propagation that occurs during the recursive computation of RPs is solved. Indeed, the proposed solution relies on the use of a new numerical method that detects unstable values and sets them to zero. This ensures the numerical stability of high-order RPs. Next, a fast method is presented to significantly reduce the required time for reconstructing large-size 1D signal. This method involves the transformation of a 1D signal into a 2D array, then using matrix reconstruction formulas in the 2D domain. The simulation and comparison results clearly show that the proposed computation methods are very useful for the fast and stable analysis of large-size signals and 2D/3D images by Racah moments (RMs). (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of variance (ANOVA) decomposition. For functions with a low-dimensional structure, i.e., a low superposition dimension, we are able to achieve a reconstruction from scattered data and simultaneously understand relationships between different variables. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We discuss a fast approximate solution to the associated classical-classical orthogonal polynomial connection problem. We first show that associated classical orthogonal polynomials are solutions to a fourth-order quadratic eigenvalue problem with polynomial coefficients such that the differential operator is degree-preserving. Upon linearization, the discretization of this quadratic eigenvalue problem is block upper-triangular and banded. After a perfect shuffle, we extend a divide-and-conquer approach to the upper-triangular and banded generalized eigenvalue problem to the blocked case, which may be accelerated by one of a few different algorithms. Associated orthogonal polynomials arise from iterated Stieltjes transforms of orthogonal polynomials; hence, fast approximate conversion to classical cases combined with fast discrete sine and cosine transforms provides a modular mechanism for synthesis of singular integral transforms of classical orthogonal polynomial expansions. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper proposes a novel hybrid FDTD method for solving the time-dependent Schrodinger equation, which is fundamental for modeling materials and designing nanoscale devices. The wave function is propagated on nonuniform grids by applying explicit updates in part of the grid and implicit updates elsewhere. The latter are based on the Alternating-Direction Implicit (ADI) scheme while the former are constructed with a central difference for the time derivative. A rigorous stability analysis proves that spatial steps can be selectively removed from the stability criterion thus combining the unconditional stability of the ADI scheme with fast explicit calculations. The scheme excels in its flexibility by efficiently discretizing and balancing explicit with implicit updates, as such expediting the computations. Moreover, it retains the linear complexity of explicit schemes with respect to space and time, making it especially scalable to numerically large problems. Several numerical experiments, including a laterally tunnel coupled quantum wire and a nanowire double-barrier resonant-tunneling diode, show the validity of the scheme by demonstrating its high accuracy and decreased CPU time compared to traditional methods. (C) 2021 Elsevier B.V. All rights reserved.
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