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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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    A new approximation algorithm for solving generalized Lyapunov matrix equations

    Shirilord, AkbarDehghan, Mehdi
    26页
    查看更多>>摘要：In this paper, we propose a new approximation algorithm for solving generalized Lyapunov matrix equations. We also present a convergence analysis for this algorithm. In each step of this algorithm two standard Lyapunov matrix equations with real coefficient matrices should be solved. Then we determine the optimal parameter to minimize the corresponding spectral radius of iteration matrix to obtain fastest speed of convergence. Finally some numerical examples are given to prove the capability of the present algorithm and a comparison is made with the existing results. (C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis

    Das, PratibhamoyRana, SubrataRamos, Higinio
    15页
    查看更多>>摘要：In this work we consider a class of fractional order Volterra integro-differential equations of first kind where the fractional derivative is considered in the Caputo sense. Here, we consider the initial value problem and the boundary value problem separately. For simplicity of the analysis, we reduce each of these problems to the fractional order Volterra integro-differential equation of second kind by using the Leibniz's rule. We have obtained sufficient conditions for the existence and uniqueness of the solutions of initial and the boundary value problems. An operator based method has been considered to approximate their solutions. In addition, we provide a convergence analysis of the adopted approach. Several numerical experiments are presented to support the theoretical results. (c) 2020 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    A combined GDM-ELLAM-MMOC scheme for advection dominated PDEs

    Droniou, JeromeLe, Kim-NganCheng, Hanz Martin
    23页
    查看更多>>摘要：We propose a combination of the Eulerian Lagrangian Localised Adjoint Method (ELLAM) and the Modified Method of Characteristics (MMOC) for time-dependent advectiondominated PDEs. The combined scheme, so-called GEM scheme, takes advantages of both ELLAM scheme (mass conservation) and MMOC scheme (easier computations), while at the same time avoids their disadvantages (respectively, harder tracking around the injection regions, and loss of mass). We present a precise analysis of mass conservation properties for these three schemes, and after achieving global mass balance, an adjustment yielding local volume conservation is then proposed. Numerical results for all three schemes are then compared, illustrating the advantages of the GEM scheme. A convergence result of the MMOC scheme, motivated by our previous work (Cheng et al., 2018), is provided which can be extended to obtain the convergence of GEM scheme. (C) 2021 The Author(s). Published by Elsevier B.V.
      原文链接:
    • NSTL
    • Elsevier

    Common solution to a pair of nonlinear Fredholm and Volterra integral equations and nonlinear fractional differential equations

    Kumar, D. Ramesh
    16页
    查看更多>>摘要：The aim of this paper is to establish the existence and uniqueness of the common solution for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations using the common fixed point results equipped with illustrative examples. Some common fixed point results satisfying the generalized contraction condition involving w-distance and weak altering distance functions are proved. Then, an example is provided to support the usability of our result along with numerical experiments. (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

    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

    Numerical solutions for Helmholtz equation with stochastic interface based on PML method

    Hao, YongleWang, LinLiu, Siyu
    12页
    查看更多>>摘要：In this paper, the stochastic interface for diffraction grating is considered and the model is formulated as the Helmholtz interface problems (HIPs). In order to have more accuracy simulation, PML boundary is used to describe the stochastic interface. Then we develop shape-Taylor expansion for the solution of HIPs, through perturbation method, we obtain the approximate simulations of second and third order. Error estimation and efficient computation of solutions by low-rank approximation are given. Finally, we illustrate these results with numerical simulations. (C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    An efficient high order iterative scheme for large nonlinear systems with dynamics

    Behl, RamandeepBhalla, SoniaMagrenan, A. A.Kumar, Sanjeev...
    16页
    查看更多>>摘要：This study suggests a new general scheme of high convergence order for approximating the solutions of nonlinear systems. The proposed scheme is the extension of an earlier study of Parhi and Gupta. This method requires two vector-function, two Jacobian matrices, two inverse matrices, and one frozen inverse matrix per iteration. Convergence error, computational efficiency, and numerical experiments are performed to verify the applicability and validity of the proposed methods compared with existing methods. Finally, we discuss the strange fixed points and conjugacy functions on a particular case of our scheme. The basins of attractions also demonstrate the dynamical behavior of this special case in the neighborhood of required roots and also assert the theoretical outcomes. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    A justification of the Darcy law for a suspension of not self-similar solid particles non-periodically distributed

    Calvo-Jurado, CarmenCasado-Diaz, JuanLuna-Laynez, Manuel
    21页
    查看更多>>摘要：We extend to a non-periodic framework the classical homogenization result permitting to derive the Darcy law from the Stokes or Navier-Stokes system posed in a perforated domain. Mathematically, we study the asymptotic behavior when epsilon tends to zero of the stationary Stokes system posed in a sequence of varying domains Omega(epsilon) = Omega \ boolean OR T-k is an element of N(epsilon)k where Omega is a smooth bounded open subset of R-3 and T-epsilon(k) are closed sets such that each of them is at a distance of order epsilon of the remaining. Moreover boolean OR T-k is an element of N(epsilon)k is at a distance of order at most epsilon of any point of R-3. Each set T-epsilon(k) is non-empty, smooth and has a size of order delta(epsilon) with epsilon(3) << delta(epsilon) <= r epsilon for some r < 1. In the classical periodic case, the sets T-epsilon(k) are obtained by repeating periodically with period epsilon the set delta T-epsilon with T a non-empty smooth closed set in R-3. As in this periodic case we show that the limit problem corresponds to a Darcy system. However, even when the sets T-epsilon(k) have all the same shape, we show that for delta(epsilon) << epsilon some strong convergence results for the velocity and some capacity formulae for the limit system do not extend from the periodic framework to the non-periodic one. (c) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Global Hessenberg and CMRH methods for a class of complex matrix equations

    Gu, YingSong, Yongzhong
    14页
    查看更多>>摘要：In this paper, we study how to use Hessenberg-based methods to solve a class of complex matrix equations, which is a general form of many known equations. A generalized global Hessenberg process is presented to construct the basis of complex matrix space. This process requires less work and storage because the basis it uses has more zero components. Then global Hessenberg (Gl-Hess) and global CMRH (Gl-CMRH) methods are proposed, which can be directly realized by the original coefficient matrices. The convergence of the Gl-CMRH method is analyzed. Numerical experiments show the efficiency of the methods and compare them with existing methods. (C) 2021 Elsevier B.V. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier