查看更多>>摘要：We introduce a new concept of convergence for iterative methods, named restricted global convergence, that consists of locating a solution and obtaining a domain of global convergence. As a consequence, results of semilocal convergence and local convergence are obtained. For this, we use auxiliary points and obtain balls of convergence. The study is illustrated with Chebyshev's method. (C) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra lambda, mu(1), mu(2) and two positive numbers beta*, beta<>. Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature.(c) 2021 Elsevier B.V. All rights reserved.
Kumar, KamaleshChakravarthy, P. PramodRamos, HiginioVigo-Aguiar, Jesus...
15页
查看更多>>摘要：This article presents a stable finite difference approach for the numerical approximation of singularly perturbed differential-difference equations (SPDDEs). The proposed scheme is oscillation-free and much accurate than conventional methods on a uniform mesh. Error estimates show that the scheme is linear convergent in space and time variables. By using the Richardson extrapolation technique, the obtained results are extrapolated in order to get better approximations. Some numerical examples are taken from literature to validate the theory, showing good performance of the proposed method. (c) 2020 Published by Elsevier B.V.
Aledo, Juan A.Diaz, Luis G.Martinez, SilviaValverde, Jose C....
14页
查看更多>>摘要：It is well known that periodic orbits with any period can appear in sequential dynamical systems over undirected graphs with a Boolean maxterm or minterm function as global evolution operator. Indeed, fixed points cannot coexist with periodic orbits of greater periods, while periodic orbits with different periods greater than 1 can coexist. Additionally, a fixed point theorem about the uniqueness of a fixed point is known. In this paper, we provide an m-periodic orbit theorem (for m > 1) and we give an upper bound for the number of fixed points and periodic orbits of period greater than 1, so completing the study of the periodic structure of such systems. We also demonstrate that these bounds are the best possible ones by providing examples where they are attained. (c) 2020 Elsevier B.V. All rights reserved.
Cordero, AliciaGarrido, NeusTorregrosa, Juan R.Chicharro, Francisco I....
15页
查看更多>>摘要：In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family is carried out on polynomial systems by selecting different weight functions and comparing the results obtained in each case. This study shows the applicability of the multidimensional dynamical analysis in order to select the methods of the family with the best stability properties. (c) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：We construct in this paper a fully-decoupled and second-order accurate numerical scheme for solving the Cahn-Hilliard-Navier-Stokes phase-field model of two-phase incompressible flows. A full decoupling method is used by introducing several nonlocal variables and their ordinary differential equation to deal with the nonlinear and coupling terms. By combining with some effective methods to handle the Navier-Stokes equation, we obtain an efficient and easy-to-implement numerical scheme in which one only needs to solve several fully-decoupled linear elliptic equations with constant coefficients at each time step. We further prove the unconditional energy stability and solvability rigorously, and present various numerical simulations in 2D and 3D to demonstrate the efficiency and stability of the proposed scheme, numerically. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Africa has long been ignored with respect to among others insurance modeling. In this paper, we propose a model for automobile claim data from Ghana. The body of the data are modeled by a lognormal distribution. However, the tail is noted be too heavy to be modeled by a single heavy tailed distribution. A mixture of distributions is used to model the tail. Estimates of risk are given. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we are concerned with the parameterized least squares inverse eigenvalue problems for the case that the number of parameters to be constructed is less than the number of prescribed realizable eigenvalues. Through equivalent transformation, the original problem becomes a nonlinear least squares problem associated with a specific over-determined mapping defined between a Riemannian manifold and a Euclidean space. We propose the Riemannian two-step perturbed Gauss-Newton method combined with a specific second-order nonmonotone backtracking line search technique for solving general nonlinear least squares problem on Riemannian manifold. Global convergence of this algorithm is discussed under some mild assumptions. Meanwhile, a cubical convergence rate is obtained under injectivity of the differential of the underlying map and zero residue of this map at an accumulation point. To apply the proposed method to solving the parameterized least squares inverse eigenvalue problems, exact solution of the perturbed Riemannian Gauss-Newton equation is constructed. Finally, numerical experiments show the efficiency of the proposed method.(c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A new class of unilateral variational models appearing in the theory of poroelasticity is introduced and studied. A poroelastic medium consists of solid phase and pores saturated with a Newtonian fluid. The medium contains a fluid-driven crack, which is subjected to non-penetration between the opposite crack faces. The fully coupled poroelastic system includes elliptic-parabolic governing equations under the unilateral constraint. Well-posedness of the corresponding variational inequality is established based on the Rothe semi-discretization in time, after subsequent passing time step to zero. The NLCP-formulation of non-penetration conditions is given which is useful for a semi-smooth Newton solution strategy. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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