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Journal of Computational and Applied Mathematics
Elsevier
Journal of Computational and Applied Mathematics

Elsevier

0377-0427

Journal of Computational and Applied Mathematics/Journal Journal of Computational and Applied MathematicsSCIISTPEI
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    Theoretical analysis of a conservative finite-difference scheme to solve a Riesz space-fractional Gross-Pitaevskii system

    Macias-Diaz, J. E.Serna-Reyes, AdnJ.
    17页
    查看更多>>摘要：In this work, we propose a fractional extension of the multi-dimensional Gross-Pitaevskii system that describes a two-component Bose-Einstein condensate with an internal atomic Josephson junction. The fractional problem is governed by two parabolic partial differential equations that consider fractional spatial derivatives of the Riesz type along with coupling terms. Initial and homogeneous Dirichlet boundary conditions are imposed on a bounded interval of a closed and bounded domain. We show that the problem can be expressed in variational form and propose a Hamiltonian function associated to the system. We prove that the total energy of the system is constant, whence the need to provide energy-conserving schemes to solve the system is pragmatically justified. Motivated by these facts, we design a finite-difference discretization of the continuous model based on the use of fractional-order centered differences. The discrete scheme has also a variational structure, and we propose a discrete form of the Hamiltonian function. As the continuous counterpart, we prove rigorously that the discrete total energy is conserved at each temporal step. The scheme is a second-order consistent discretization of the continuous model. Moreover, we prove the stability and quadratic convergence of the numerical model. We provide some computer simulations using an implementation of our scheme to illustrate the validity of the conservation properties. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Reliability estimation of s-out-of-k system in a multicomponent stress-strength dependent model based on copula function

    Zhu, Tiefeng
    11页
    查看更多>>摘要：In reliability analysis of the traditional stress-strength models, the stress and strength are often assumed to be independent variables. However the case where this two variables are dependent is more realistic in engineering. To evaluate multicomponent system reliability in such case, the stress and strength are assumed to have dependent Kumaraswamy variable and unit Gompertz variable based on Clayton copula. Then the maximum likelihood (ML), least squares (LS), maximum product of spacings (MPS), Cramer-von-Mises and LS (CL) hybrid estimates of the unknown parameters and system reliability are derived using two-step estimation procedure under order sample. Also the asymptotic distribution of the ML estimation and the parametric bootstrap percentile method are used to construct approximate confidence intervals (CI). Moreover, Monte Carlo simulations are implemented to compare the performance of the proposed methods. Finally, one real data set is analyzed for illustrative purposes. (C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    An alternative method to construct a consistent second-order theory on the equilibrium figures of rotating celestial bodies

    Orti, Jose A. LopezGumbau, Manuel FornerRochera, Miguel Barreda
    14页
    查看更多>>摘要：The main objective of this work is to construct a new method to develop a consistent second-order amplitudes theory to evaluate the potential of a rotating deformable celestial body when the hydrostatic system equilibrium has been achieved. In this case, -we have: (sic) P rho & nbsp;(SIC) Psi, delta Psi = -4 pi Gp +2w(2), where P is the pressure, p is the density, (SIC)is the total potential, A is Laplace operator, G is the gravitational constant and & RARR;-w is the angular velocity of the system. To integrate these equations in a general case of mass distribution a state equation relating pressure and density is needed.& nbsp;To assess the full potential, Psi, it is necessary to calculate the self-gravitational potential, omega, and the centrifugal potential, V-c. The equilibrium configuration involves the hydrostatic equilibrium, it is, the rigid rotation of the system corresponding to the minimum potential and, according to Kopal, this state involves the identification of equipotential, isobaric, isothermal and isopycnic surfaces.& nbsp;To study the structure of the body we define a coordinate system OXYZ where O is the center of mass of the component, OX is an axis fixed in an arbitrary point of the body equator, OZ an axis parallel to angular velocity (SIC)& nbsp;and OY defining a direct trihedron. For an arbitrary point P in the rotating body the Clairaut coordinates are given by (a, theta, lambda) where a is the radius of the sphere that contains the same mass that the equipotential surface that contains P and (theta, lambda) are the angular spherical coordinates of P.& nbsp;This problem has been solved in the first order in w2 following two techniques: the first one is based on the asymptotic properties of the numerical quadrature formulae. The second is similar to the one used by Laplace to develop the inverse of the distance between two planets. The second-order theory based on the first method has been developed by the authors in a recent paper. In this work we develop a consistent second-order theory about the equilibrium figures of rotating celestial bodies based on the second method.& nbsp;Finally, to show the performance of the method it is interesting to study a numerical example based on a convective star. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Analysis of a nonlinear singularly perturbed Volterra integro-differential equation

    Sumit, SunilKumar, SunilVigo-Aguiar, Jesus
    13页
    查看更多>>摘要：We consider a nonlinear singularly perturbed Volterra integro-differential equation. The problem is discretized by an implicit finite difference scheme on an arbitrary nonuniform mesh. The scheme comprises of an implicit difference operator for the derivative term and an appropriate quadrature rule for the integral term. We establish both a priori and a posteriori error estimates for the scheme that hold true uniformly in the small perturbation parameter. Numerical experiments are performed and results are reported for validation of the theoretical error estimates. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Local averaging type a posteriori error estimates for the nonlinear steady-state Poisson-Nernst-Planck equations

    Yang, YingShen, RuigangFang, MingjuanShu, Shi...
    30页
    查看更多>>摘要：The a posteriori error estimates are studied for a class of nonlinear stead-state Poisson-Nernst-Planck equations, which are a coupled system consisting of the Nernst-Planck equation and the Poisson equation. Both the global upper bounds and the local lower bounds of the error estimators are obtained by using a local averaging operator. Numerical experiments are given to confirm the reliability and efficiency of the error estimators. (C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Analysis of the distribution of times of escape in the N-body ring problem

    Navarro, Juan F.Martinez-Belda, M. C.
    14页
    查看更多>>摘要：This paper summarizes the results of a numerical investigation of the phenomenon of escape in the N-body ring problem. There is a value of the Jacobi constant of the system such that for smaller values, the potential well opens and test particles may leave the potential through any of its N openings. By means of a surface of section, we show the results of the computation of the basins of escape towards the different directions for N = 5, 6, 7, 8. We have also analyzed the percentage of escaping orbits, the direction of escape and the distribution of the times of escape.(C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Convergence, stability analysis, and solvers for approximating sublinear positone and semipositone boundary value problems using finite difference methods

    Lewis, ThomasZhang, YiMorris, Quinn
    22页
    查看更多>>摘要：Positone and semipositone boundary value problems are semilinear elliptic partial differ-ential equations (PDEs) that arise in reaction-diffusion models in mathematical biology and the theory of nonlinear heat generation. Under certain conditions, the problems may have multiple positive solutions or even nonexistence of a positive solution. We develop analytic techniques for proving admissibility, stability, and convergence results for simple finite difference approximations of positive solutions to sublinear problems. We also develop guaranteed solvers that can detect nonuniqueness for positone problems and nonexistence for semipositone problems. The admissibility and stability results are based on adapting the method of sub-and supersolutions typically used to analyze the underlying PDEs. The new convergence analysis technique directly shows that all pointwise limits of finite difference approximations are solutions to the boundary value problem eliminating the possibility of false algebraic solutions plaguing the convergence of the methods. Most known approximation methods for positone and semipositone boundary value problems rely upon shooting techniques; hence, they are restricted to one-dimensional problems and/or radial solutions. The results in this paper will serve as a foundation for approximating positone and semipositone boundary value problems in higher dimensions and on more general domains using simple approximation methods. Numerical tests for known applied problems with multiple positive solutions are pro-vided. The tests focus on approximating certain positive solutions as well as generating discrete bifurcation curves that support the known existence and uniqueness results for the PDE problem. (c) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    On the distribution of the likelihood ratio test of independence for random sample size - a computational approach

    Coelho, Carlos A.Jorge, NadabNunes, CeliaMarques, Filipe J....
    20页
    查看更多>>摘要：The test of independence of two groups of variables is addressed in the case where the sample size N is considered randomly distributed. This assumption may lead to a more realist testing procedure since in many situations the sample size is not known in advance. Three sample schemes are considered where N may have a Poisson, Binomial or Hypergeometric distribution. For the case of two groups with p(1) and p(2) variables, it is shown that when either p(1) or p(2) (or both) are even the exact distribution corresponds to a finite or an infinite mixture of Exponentiated Generalized Integer Gamma distributions. In these cases a computational module is made available for the cumulative distribution function of the test statistic. When both p(1) and p(2) are odd, the exact distribution of the test statistic may be represented as a finite or an infinite mixture of products of independent Beta random variables whose density and cumulative distribution functions do not have a manageable closed form. Therefore, a computational approach for the evaluation of the cumulative distribution function is provided based on a numerical inversion formula originally developed for Laplace transforms. When the exact distribution is represented through infinite mixtures, an upper bound for the error of truncation of the cumulative distribution function is provided. Numerical studies are developed in order to analyze the precision of the results and the accuracy of the upper bounds proposed. A simulation study is provided in order to assess the power of the test when the sample size N is considered randomly distributed. The results are compared with the ones obtained for the fixed sample size case. (C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    A two-parameter Milstein method for stochastic Volterra integral equations

    Li, MinHuang, ChengmingWen, Jiao
    20页
    查看更多>>摘要：In this paper, a two-parameter Milstein method for stochastic Volterra integral equations is introduced. First, the method is proved to be strongly convergent with order one in L-p norm (p >= 1). Then, we investigate the mean square stability of the exact and numerical solutions of a stochastic convolution test equation. Stability conditions are derived. Based on these conditions, analytical and numerical stability regions are plotted and compared with each other. The results show that additional implicitness offers benefits for numerical stability. Finally, some numerical experiments are carried out to confirm the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Impact of local congruences in variable selection from datasets

    Aragon, Roberto G.Medina, JesusRamirez-Poussa, Eloisa
    14页
    查看更多>>摘要：Formal concept analysis (FCA) is a useful mathematical tool for obtaining information from relational datasets. One of the most interesting research goals in FCA is the selection of the most representative variables of the dataset, which is called attribute reduction. Recently, the attribute reduction mechanism has been complemented with the use of local congruences in order to obtain robust clusters of concepts, which form convex sublattices of the original concept lattice. Since the application of such local congruences modifies the quotient set associated with the attribute reduction, it is fundamental to know how the original context (attributes, objects and relationship) has been modified in order to understand the impact of the application of the local congruence in the attribute reduction. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier