查看更多>>摘要：In this paper, we consider a class of parameterized singularly perturbed problems with integral boundary condition. A finite difference scheme of hybrid type with an appropriate Shishkin mesh is suggested to solve the problem. We prove that the method is of almost second order convergent in the discrete maximum norm. Numerical results are presented, which illustrate the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We introduce a family of symmetric stochastic Bernstein polynomials based on order statistics, and establish the order of convergence in probability in terms of the second order Ditzian-Totik type modulus of smoothness on the interval [0, 1], which epitomizes an optimal pointwise error estimate for the classical Bernstein polynomial approximation. Monte Carlo simulation results (presented at the end of the article) show that this new approximation scheme is efficient and robust. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we design a numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space- time. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0, 1) boolean OR (1, 2], which considers a generalized potential and a time-dependent diffusion factor. An energy integral for the mathematical model is readily available, and we propose an explicit and consistent numerical technique based on fractional-order centered differences with similar Hamiltonian properties as the continuous model. A fractional energy approach is used then to prove the properties of stability and convergence of the technique. For simulation purposes, we consider both the classical and the fractional Higgs real-valued scalar fields in the (3 + 1)-dimensional de Sitter space-time, and find results qualitatively similar to those available in the literature. The present work is the first paper to report on a Hamiltonian discretization of the Higgs boson equation (both fractional and non-fractional) in the de Sitter space-time and its numerical analysis. More precisely, the present manuscript is the first paper of the literature in which a dissipation-preserving scheme to solve the multi-dimensional (fractional) Higgs boson equation in the de Sitter space-time is proposed and thoroughly analyzed. Indeed, it is worth pointing out that previous efforts used techniques based on the Runge-Kutta method or discretizations that did not preserve the dissipation nor were rigorously analyzed. (c) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper is concerned with an efficient numerical method for solving the 1D stationary Schrodinger equation in the highly oscillatory regime. Being a hybrid, analytical- numerical approach it does not have to resolve each oscillation, in contrast to standard schemes for ODEs. We build upon the WKB-based (named after the physicists Wentzel, Kramers, Brillouin) marching method from Arnold et al. (2011) and extend it in two ways: By comparing the O(h) and O(h(2)) methods from Arnold et al. (2011) we design an adaptive step size controller for the WKB method. While this WKB method is very efficient in the highly oscillatory regime, it cannot be used close to turning points. Hence, we introduce for such regions an automated methods switching, choosing between the WKB method for the oscillatory region and a standard Runge-Kutta-Fehlberg 4(5) method in smooth regions. A similar approach was proposed recently in [Handley et al. (2016), Agocs et al. (2020)], however, only for an O(h)-method. Hence, we compare our new strategy to their method on two examples (Airy function on the spatial interval [0, 10(8)] with one turning point at x = 0 and on a parabolic cylinder function having two turning points), and illustrate the advantages of the new approach w.r.t. accuracy and efficiency. (C) 2021 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：We consider a class of singularly perturbed degenerate parabolic convection-diffusion problems on a rectangular domain. A numerical method is constructed using the implicit Euler scheme on a uniform mesh in the time direction and the upwind finite difference scheme on a layer adaptive non-uniform mesh in the spatial direction. The layer adaptive non-uniform mesh in the spatial direction is generated through the equidistribution of a suitably chosen monitor function. We perform error analysis through the truncation error and barrier function approach and prove that the method is uniformly convergent with first order in both time and space. Numerical results are given in support of theoretical findings. (C) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we put forward a new spectral element method for the nonlinear second-kind Volterra integral equations (VIEs) with weakly singular kernel, which employs shifted Muntz-Jacobi functions and shifted Legendre polynomials as basis functions. This method is capable of approximating the limited regular solution more efficiently. We analyze the existence and uniqueness of the solution to the numerical scheme and derive the hp-version optimal convergence under some reasonable assumptions. A series of numerical examples are presented to demonstrate the efficiency of the new method. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We propose an efficient iterative scheme to solve numerically a quadratic matrix equation related to the noisy Wiener-Hopf problems for Markov chains. We improve the efficiency and the accuracy of the well-known Newton's method, frequently used in the literature. We provide a semilocal convergence result for this iterative scheme, where we establish domains of existence and uniqueness of solution. Finally, we apply this efficient method to approximate the solution of a particular noisy Wiener-Hopf problem and we compare it with Newton's method. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Recently, Yang et al. (2020) established the strong convergence of the truncated Euler-Maruyama (EM) approximation, that was first proposed by Mao (2015), for onedimensional stochastic differential equations with superlinearly growing drift and the Holder continuous diffusion coefficients. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is to construct several new techniques of the partially truncated EM method to establish the optimal convergence rate in theory without these restrictions. The other aim is to study the stability of the partially truncated EM method. Finally, some simulations and examples are provided to support the theoretical results and demonstrate the validity of the approach. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we study a coefficient identification problem described by an elliptic variational-hemivariational inequality with unilateral constraints. The inequality is the weak formulation of the mathematical model of a stationary incompressible flow of Bingham type in a bounded domain. The unknown coefficient is a generalized viscosity function of the fluid. The boundary conditions represent generalizations of the no leak condition and a multivalued and nonmonotone version of a nonlinear Navier-Fujita frictional slip condition. The result on well posedness of the direct problem is established based on the theory of multivalued pseudomonotone operators. The existence to the inverse problem is proved by a Weierstrass type argument. (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/).
查看更多>>摘要：Monitoring multiple parameters of a process using a single integrated charting scheme is an attractive research area in statistical process monitoring and control. The Max-type combining function based on Chebyshev's distance and the Distance-type combining function, essentially based on Euclidean distance, are widely used to construct various schemes for simultaneously monitoring the location and scale parameters. In most of these schemes, normalising the suitable function of maximum likelihood estimators (MLE) of individual parameters is commonly used. While monitoring two-parameter exponential distributions, we show that mapping the pivots based on the maximum likelihood estimators to standard normal variables is not optimal. This paper investigates four different mappings to analyse the transformation effect on the joint monitoring schemes for a two-parameter exponentially distributed process. The Chebyshev's and Euclidean distances are particular cases of Minkowski distance. We additionally investigate the effect of Manhattan and minimum-type Minkowski distances via Monte Carlo in terms of the run-length properties. The overall chart performance is assessed using the expected weighted run length (EWRL). It is observed that the use of Manhattan distance and mapping into the standard Laplace model is more appropriate. A real example of monitoring a high-voltage current in a P-type high-voltage metal oxide semiconductor transistor (HPM) data is given to show the excellent performance of the suggested control chart. (C) 2021 Elsevier B.V. All rights reserved.
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