Occorsio, DonatellaRusso, Maria GraziaThemistoclakis, Woula
19页
查看更多>>摘要：A product quadrature rule, based on the filtered de la Vallee Poussin polynomial approximation, is proposed for evaluating the finite weighted Hilbert transform in [-1, 1]. Convergence results are stated in weighted uniform norm for functions belonging to suitable Besov type subspaces. Several numerical tests are provided, also comparing the rule with other formulas known in literature. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepping strategies which work by reducing the stepsize as solutions approach a neighbourhood of zero. The method is hybrid in the sense that a convergent backstop method is invoked if the timestep becomes too small, or to prevent solutions from overshooting zero and becoming negative. Under parameter constraints that imply Feller's condition, we prove that such a scheme is strongly convergent, of order at least 1/2. Control of the strong error is important for multi-level Monte Carlo techniques. Under Feller's condition we also prove that the probability of ever needing the backstop method to prevent a negative value can be made arbitrarily small. Numerically, we compare this adaptive method to fixed step implicit and explicit schemes, and a novel semi-implicit adaptive variant. We observe that the adaptive approach leads to methods that are competitive in a domain that extends beyond Feller's condition, indicating suitability for the modelling of stochastic volatility in Heston-type asset models. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：In this article, we introduce the predictive estimation approach for estimating the population mean using modified difference and ratio type predictive estimators in ranked set sampling. The expressions of bias and mean square error of the proffered predictive estimators are reported to the first order of approximation. A comparative study of the proffered predictive estimators with the conventional predictive estimators under simple random sampling and ranked set sampling is considered. The theoretical findings have been supported by a broad spectrum computational study carried out using various real and simulated data sets. Further, the appropriate suggestions are forwarded to the survey professionals. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose a Virtual Element Method (VEM) for the Laplacian eigenvalue problem, which is designed to avoid the requirement of the stabilization terms in standard VEM bilinear forms. In the present method, the constructions of the bilinear forms depend on higher order polynomial projection. To exactly compute the bilinear forms, we need to modify the virtual element space associated to the higher order polynomial projection. Meanwhile, the continuity and coercivity of the discrete VEM bilinear forms depend on the number of vertices of the polygon. By the spectral approximation theory of compact operator and the projection and interpolation error estimates, we prove correct spectral approximation and error estimates for the VEM discrete scheme. Finally, we show numerical examples to verify the theoretical results, including the Laplace eigenvalue problem and the Steklov eigenvalue problem. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：First, we study the superconvergence properties of the prolate interpolation and differen-tiation. Advantages over the polynomial-based results can be observed in approximating and solving differential equation. Then we propose the fast implementation of the second order barycentric prolate differentiation by the fast multipole method (FMM) and the optimal convergence rate is given. Effectiveness and accuracy of the proposed method are tested by numerical examples.(C) 2022 Elsevier B.V. All rights reserved.
Jothilakshmi, G.Vadivoo, B. S.Almalki, Y.Debbouche, A....
14页
查看更多>>摘要：We study the controllability criteria for a class of fractional integro-differential damped systems with impulsive perturbations. The solution representation is derived for both linear and non-linear damped systems, and the introduced formulations were constructed by employing Laplace transformation with Mittag-Leffler matrix function. We present necessary and sufficient conditions for the indicated systems to be controllable in finite dimensional spaces. Here, controllability conditions are proposed by using Grammian matrix as a powerful tool. Two numerical examples are also given at end to demonstrate the obtained theory. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions is considered. Some special cases for this distribution, such as generalized skew-normal, generalized skew student -t, generalized skew-logistic and generalized skew-Laplace distributions, are also considered. In order to test the theoretical feasibility of our results, the MTCov for skewed and non skewed normal distributions is computed and compared. Finally, we give a special formula of the MTCov for generalized skew-elliptical distributions. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, Spalevic derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. Numerical experiments reported in this paper show both kinds of averaged rules to often give much higher accuracy than can be expected from their degrees of exactness. This is important when estimating the error in a Gauss rule by an associated averaged rule. We use techniques similar to those employed by Trefethen in his investigation of Clenshaw-Curtis rules to shed light on the performance of the averaged rules. The averaged rules are not guaranteed to be internal, i.e., they may have nodes outside the convex hull of the support of the measure. This paper discusses three approaches to modify averaged rules to make them internal.(c) 2022 Elsevier B.V. All rights reserved.
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