查看更多>>摘要：In this article, we develop a least-squares/fictitious domain method for direct simulation of fluid particle motion with Navier slip boundary condition at the fluid-particle interface. Let Omega and B be two bounded domains of R-d such that B subset of Omega. The motion of solid particle B is governed by Newton's equations. Our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the full Omega, followed by a well-chosen correction over B and corrections related to translation velocity and angular velocity of the particle. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Since the fully explicit scheme to update the particle motion using Newton's equation is unstable, we propose and implement an explicit-implicit scheme in which, at each time step, the position of the particle is updated explicitly, and the solution of Navier-Stokes equations and particle velocities are solved by the the least-squares/fictitious domain method implicitly. Numerical results are given to verify our numerical method. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, wavelet optimized finite difference B-spline polynomial chaos method is proposed for solving stochastic partial differential equations. The generalized polynomial chaos is applied by considering linear B-spline wavelet basis. Then, stochastic Galerkin projection is executed for evaluating the deterministic coefficients of the generalized polynomial chaos. In the next step, the system of equations is discretized by using Crank-Nicolson scheme for time integration and for approximating the differential operators, central finite difference matrices are considered. An adaptive grid is generated using the linear B-spline generalized polynomial chaos for optimizing the numerical solution. The method is then tested on three problems namely heat equation with uncertain initial conditions, Burger's equation with random initial conditions and Burger's equation with random viscosity as well as uncertain initial conditions. For the three test problems, grid modifications are displayed by taking periodic boundary conditions into consideration. Mean and standard deviation are plotted for each test problem. Moreover, for the third test problem, computational time comparison is performed by computing CPU time taken by the proposed method and the CPU time taken by the finite difference method on a uniform grid. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Hybrid difference methods are a kind of finite difference methods which is similar to hybrid discontinuous Galerkin methods introduced by Jeon and Park (SIAM J. Numer. Anal., 2010). In the previous hybrid difference method, the approximate solution is only defined on the lines parallel to the coordinate axes, but the approximation is not defined at the corner/edge nodes. Thus, it is hard to calculate the approximation value without loosing accuracy at any point in the domain due to the aforementioned missing information. To overcome this issue, we first propose a novel hybrid difference method by imposing some conditions to determine the missing information. With this, we are able to provide not only continuous approximations in the whole domain, but also the gradient of the numerical solution becomes continuous under certain conditions. Next, we prove that the proposed method is stable and locally conservative. The proposed method can be also viewed as the existing hybrid difference method with a simple postprocessing. The postprocessing not only induces a simple tridiagonal system on each mesh line, but also it can be done efficiently line by line or in parallel. Lastly, a reliable and efficient a posteriori error estimate is established for computational efficiency. Several numerical results are presented to confirm our findings. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We deal with the statistical structure of data losses, when packetized data are transmitted through a channel with a buffering mechanism and may be subject to losses due to the buffer overflow. The main contribution is an explicit formula for the burst ratio parameter, which reflects the tendency of losses to cluster together, in long series. A general model of the arrival stream is used, which enables arbitrary shaping of the interarrival time distribution and the autocorrelation function of interarrival times. In numerical examples, the dependence of the burst ratio on various model parameters is shown, with a special attention to the impact of the autocorrelation of the arrival process. Some unexpected, counterintuitive observations are made. (C) 2021The Author(s). Published by Elsevier Inc.
查看更多>>摘要：Determining how many limit cycles a planar polynomial system of differential equations can have is a remarkably hard problem. One of the main difficulties is that the limit cycles can reside within areas of vastly different scales. This makes numerical explorations very hard to perform, requiring high precision computations, where the necessary precision is not known in advance. Using rigorous computations, we can dynamically determine the required precision, and localize all limit cycles of a given system. We prove that the Songling system of planar, quadratic polynomial differential equations has exactly four limit cycles. Furthermore, we give precise bounds for the positions of these limit cycles using rigorous computational methods based on interval arithmetic. The techniques presented here are applicable to the much wider class of real-analytic planar differential equations. (C) 2021 The Authors. Published by Elsevier Inc.
查看更多>>摘要：This paper presents a new state-dependent switching strategy for stabilization of switched time-delay systems with all subsystems being unstable. When time-delays are not small enough, the delayed subsystem can be approximated as a third-order linear delay-free system by using third-order Taylor expansion. Then, a special vibration model with a nonholonomic constraint is introduced to match the obtained third-order linear system. On this basis, the energy function of the original delayed subsystem is constructed by the sum of the kinetic and potential energies of the special vibration model. After that, a state-dependent switching rule with large energy loss in a switching loop is designed by using the energy functions of two delayed subsystems. Finally, excellent agreement is found between our analytical results and the corresponding numerical simulations. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Various novel expressions of weak core inverse and its dual are developed in this paper. In addition, integral and limit representations as well as perturbation formulae for the weak core and dual weak core inverses are presented. We investigate continuity for the weak core inverse and its dual. The weak core and dual weak core inverses for upper block triangular matrix are considered. A variant of the successive matrix squaring computational iterative scheme is given for calculating the weak core inverse. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：American option pricing plays an essential role in quantitative finance and has been extensively studied in the past. However, how transaction costs affect the American option price, particularly the most important feature of American options, the optimal exercise price, is much less investigated. It is primarily because such a study must be conducted under an incomplete market, which presents additional difficulties on top of an already difficult nonlinear mathematical problem. This paper attempts to provide a supplement study in this area by analyzing the optimal exercise price of an American option in addition to the option price itself in the presence of transaction costs through a utility-based approach. With a computationally efficient numerical scheme, we are able to demonstrate clearly how the optimal exercise price should be calculated and consequently how the option prices for the buyer and writer as well as the early exercise decision are affected by the inclusion of transaction cost. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this article, multiple delay-dependent event-triggered finite-time H-infinity filtering as well as fault-tolerant control is discussed for networked random systems subject to state as well as input constraints. This is the first time to explore fault detection issue via filtering for networked random models. First, an event-triggered scheme is designed. Secondly, a zero order holder is studied. According to this event-triggered mechanism, a fault detection filter, a fault weighting system and a controller are investigated for the networked random system. And then an augmented system can be got. Sufficient conditions of mean-square finite-time boundedness with input-output finite-time mean square stabilization can be provided through the framework of linear matrix inequalities. Finally, these effectiveness and merits are verified by an example. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We develop a rigorous numerical method for periodic solutions of impulsive delay differential equations, as well as parameterized branches of periodic solutions. We are able to compute approximate periodic solutions to high precision and with computer-assisted proof, verify that these approximate solutions are close to true solutions with explicitly computable error bounds. As an application, we prove the existence of a global branch of periodic solutions in the pulse-harvested Hutchinson equation, connecting the state at carrying capacity in the absence of harvesting to the transcritical bifurcation at the extinction steady state. (C) 2021 Elsevier Inc. All rights reserved.
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