查看更多>>摘要：Departing from a two-dimensional parabolic system that describes the spatial dynamics in a predator-prey system with Michaelis-Menten-type functional response, we investigate a general form of that model using a finite-difference approach. The model under investigation is a hyperbolic nonlinear system consisting of two coupled partial differential equations with generalized reaction terms. We impose initial conditions on a closed and bounded rectangle, and a fully discrete finite-difference methodology is proposed. Among the most important results of this work, we establish analytically the existence and uniqueness of discrete solutions, along with the second-order consistency of our scheme. Moreover, a discrete form of the energy method is employed to prove the stability and the quadratic convergence of the technique. Some numerical simulations obtained through our method show the appearance of Turing patterns in the parabolic case, in agreement with some reports found in the literature. Moreover, our simulations also show that Turing patterns are present in the hyperbolic scenario. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider a space-time adaptive splitting scheme for polycrystallization processes described by a two-field phase field model. The phase field model consists of a coupled system of evolutionary processes for the local degree of crystallinity phi and the orientation angle Theta one of them being of first order total variation flow type. The splitting scheme is based on an implicit discretization in time which allows a decoupling of the system in the sense that at each time step minimization problems in phi and Theta have to be solved successively. The discretization in space is taken care of by a standard finite element approximation for the problem in phi and an Interior Penalty Discontinuous Galerkin (IPDG) approximation for the one in Theta. The adaptivity in space relies on equilibrated a posteriori error estimators for the discretization errors in phi and Theta in terms of primal and dual energy functionals associated with the respective minimization problems. The adaptive time stepping is dictated by the convergence of a semismooth Newton method for the numerical solution of the nonlinear problem in Theta. Numerical results illustrate the performance of the adaptive space-time splitting scheme for two representative polycrystallization processes. (C) 2021 Elsevier B.V. All rights reserved.
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.
查看更多>>摘要：Almost strictly sign regular matrices are sign regular matrices with a special zero pattern and whose nontrivial minors are nonzero. In this paper we provide several properties of almost strictly sign regular rectangular matrices of maximal rank and analyze their QR factorization. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
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.
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.
Cortes, J. -C.Navarro-Quiles, A.Romero, J. -V.Rosello, M. -D....
18页
查看更多>>摘要：This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise. (C) 2021 Elsevier B.V. All rights reserved.
Defez, E.Ibanez, J.Alonso-Jorda, P.Alonso, Jose M....
16页
查看更多>>摘要：We present in this paper a new method based on Bernoulli matrix polynomials to approximate the exponential of a matrix. The developed method has given rise to two new algorithms whose efficiency and precision are compared to the most efficient implementations that currently exist. For that, a state-of-the-art test matrix battery, that allows deeply exploring the highlights and downsides of each method, has been used. Since the new algorithms proposed here do make an intensive use of matrix products, we also provide a GPUs-based implementation that allows to achieve a high performance thanks to the optimal implementation of matrix multiplication available on these devices. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we study a two-grid method based on discontinuous Galerkin discretization for the convection-diffusion-reaction equation. The two-grid algorithm consists two steps: first solving the original nonsymmetric problem on coarse grid, and then solving the corresponding positive definite diffusion problem on fine grid. Note that the number of degrees of freedom on coarse mesh is less than the ones on fine mesh. Moreover, the bilinear form of positive definite problem on fine mesh only depends on the diffusion coefficient. Therefore, the two-grid algorithm essentially transforms the DG solution of convection-diffusion-reaction equation into the approximation for the DG solution of diffusion equation. The corresponding error estimates of the two-grid solution are also provided. Numerical experiments are performed to verify the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
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