查看更多>>摘要：We survey some polynomials {P-n} arising from convergence acceleration, and numerical integration, that satisfy "biorthogonality" conditions such as integral(b)(a) P-n (x) phi(j) (x) w (x) dx = 0, for appropriate functions {phi(j)} and weights w. One example is phi(j) (x) = (log x)(j) , 0 <= j <= n - 1 on [a, b] = [0, 1]. We discuss identities, asymptotics, positive quadratures, and zero distributions. We also list some open questions. (c) 2021 Elsevier B.V. All rights reserved.
Dinariev, O. YuRego, L. A. PessoaBedrikovetsky, P.
26页
查看更多>>摘要：This paper develops a modified version of the Boltzmann's equation for micro-scale particulate flow with capture and diffusion that describes the colloidal-suspension nano transport in porous media. An equivalent sink term is introduced into the kinetic equation instead of non-zero initial data, resulting in the solution of an operator equation in the Fourier space and an exact homogenization. The upper scale equation is obtained in closed form together with explicit formulae for the large-scale model coefficients in terms of the micro-scale parameters. The upscaling reveals the delay in particle transport if compared with the carrier water velocity, which is a collective effect of the particle capture and diffusion. The derived governing equation generalizes the current models for suspension-colloidal-nano transport in porous media. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, an efficient algorithm is proposed for solving convex constrained equations. The method has the following characteristics: (i) its search direction satisfies the sufficient descent property which is independent of any line search conditions; (ii) the equations only satisfy pseudo-monotone property; (iii) its global convergence is proved without the Lipschitz continuity. We compare our numerical results for test problems with those of other derivative-free projection methods. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we consider the numerical approximations for the Cahn-Hilliard-Hele- Shaw system, which is a modified Cahn-Hilliard equation coupled with the Darcy flow law. One of challenges in solving this system numerically is how to develop linear discretization for the nonlinear term, while preserving the energy stability. By introduc-ing a Lagrange multiplier r, we construct a fully discrete, second-order linear scheme. The proposed scheme is rigorously proven to be uniquely solvable and unconditionally stable in energy. Moreover, we show theoretical analysis on error estimates of the time step size Tau and space step size h at the discrete level. Several numerical examples are presented to demonstrate the stability, accuracy and efficiency of the proposed scheme. We also show numerical simulations on the coarsening dynamics. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The 2D-model of an elastic body with a finite set of rigid inclusions is considered. We assume that the body can come in frictionless contact on a part of its boundary with a rigid obstacle. On the remaining part of the body's boundary a homogeneous Dirichlet boundary condition is imposed. For a family of corresponding variational problems, we analyze the dependence of their solutions on locations of the rigid inclusions. Continuous dependency of the solutions on location parameters is established. The existence of a solution of the optimal control problem is proven. For this problem, a cost functional is defined by an arbitrary continuous functional on the solution space, while the control is given by location parameters of the rigid inclusions. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Iterative soft thresholding algorithm (ISTA) has a simple formulation and it can easily be implemented. Nevertheless, ISTA is limited to well-conditioned problems, e.g. compressive sensing. In this paper, we present an ISTA type algorithm based on the generalized conditional gradient method (GCGM) to solve elastic-net regularization which is commonly adopted in ill-conditioned problems. Furthermore, we propose a projected gradient (PG) method to accelerate the ISTA type algorithm. In addition, we discuss the existence of the radius R and we give a strategy to determine the radius R of the l1-ball constraint in the PG method by Morozov's discrepancy principle (MDP). Numerical results are reported to illustrate the efficiency of the proposed approach. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We describe a stable and efficient algorithm for computing positive suboptimal extensions of the Gaussian quadrature rule with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. These rules constitute a particular case of those first considered by Begumisa and Robinson (1991) and then by Patterson (1993) and have been proven to verify asymptotically good properties for a large class of weight functions. In particular, they may exist when the Gauss-Kronrod rule does not. The proposed algorithm is a nontrivial modification of the one introduced by Laurie (1997) for the Gauss-Kronrod quadrature, and it is based on the determination of an associated Jacobi matrix. The nodes and weights of the rule are then given as the eigenvalues and eigenvectors of the matrix, as in the classical Golub-Welsch algorithm (1969). (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we study the numerical solution for the evolutionary stable distribution (ESD) model. A new implicit-explicit scheme is proposed to discretize the ESD model, which can keep the numerical solution unconditionally positive at each time step. Moreover, it is theoretically proved that the proposed scheme satisfies the property of the entropy dissipation. Numerical experiments are carried out to demonstrate the numerical accuracy and the effectiveness of the proposed scheme. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this article, a step-by-step collocation technique based on the Jacobi polynomials is considered to solve a class of neutral delay fractional stochastic differential equations (NDFSDEs). First, we convert the NDFSDE into a non-delay equation by applying a stepby-step method. Then, by using a Jacobi collocation technique in each step, a non-delay nonlinear system is obtained. The convergence analysis of this numerical technique is discussed. Finally, several examples are implemented to confirm the efficiency and effectiveness of the proposed method. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose a two-step procedure to estimate tail-related risks like VaR and ES for the GARCH model. We inventively put forward the composite asymmetric least squares (CALS) regression to estimate the volatility structure and distinguish it from the innovation process in the GARCH model. Then noting that expectile bridges the gap between VaR and ES, we introduce the empirical likelihood method to determine these relations. Accordingly, a new optimization algorithm is proposed. Compared with the existing grid-search method, this new proposed method is data-driven and distribution free, and shares better estimation accuracy and computational efficiency. Monte Carlo simulation studies and empirical analysis also indicate that our proposed method is superior to some alternative existing tail-related risk estimation methods. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier