查看更多>>摘要：When using high-order schemes to solve hyperbolic conservation laws in bounded do-mains, it is necessary to properly treat boundary conditions so that the overall accuracy and stability are maintained. In [1, 2] a finite difference boundary treatment method is proposed for Runge-Kutta methods of hyperbolic conservation laws. The method combines an inverse Lax-Wendroff procedure and a WENO type extrapolation to achieve desired ac-curacy and stability. In this paper, we further develop the boundary treatment method for high-order linear multistep methods (LMMs) of hyperbolic conservation laws. We test the method through both 1D and 2D benchmark numerical examples for two third-order LMMs, one with a constant time step and the other with a variable time step. Numeri-cal examples show expected high order accuracy and excellent stability. In addition, the approach in [3] may be adopted to deal with an exceptional case where eigenvalues of the flux Jacobian matrix change signs at the boundary. These results demonstrate that the combined boundary treatment method works very well for LMMs of hyperbolic conserva-tion laws. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The exact solutions to nonlinear fractional problems usually have initial singularity. Taking the singularity into account, the change of variable and the block-by-block approach are introduced to propose a novel high-order scheme. It is proved that our proposed scheme can be of order 3 + alpha under the non-smooth solutions. Numerical examples are shown to validate our theoretical results. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This work presents a study of Liu-Storey (LS) nonlinear conjugate gradient (CG) methods to solve vector optimization problems. Three variants of the LS-CG method originally designed to solve single-objective problems are extended to the vector setting. The first algorithm restricts the LS conjugate parameter to be nonnegative and use a sufficiently accurate line search satisfying the (vector) standard Wolfe conditions. The second algorithm combines a modification in the LS conjugate parameter with a line search satisfying the (vector) strong Wolfe conditions. The third algorithm consists of a combination of the LS conjugate parameter with a new Armijo-type line search (to be proposed here for the vector setting). Global convergence results and numerical experiments are presented.(c) 2022 Elsevier Inc. All rights reserved.
Oliveira, Pedro M.Palma, Jonathan M.Lacerda, Marcio J.
13页
查看更多>>摘要：This paper investigates the packet-based state-feedback control problem for uncertain discrete-time cyber-physical systems. The presence of Denial of Service (DoS) attacks is considered, and the dynamics of the closed-loop system under attacks is modeled as a switched uncertain system. The 7/ 2 performance criteria is employed to assess the robustness of the system. Moreover, three strategies are considered in the control design: i) the use of a full packet of controllers, ii) the zero-input strategy, which sets the control to zero in the presence of an attacker, and iii) the hold strategy, that keeps the same control input during the DoS attack. The conditions are formulated as parameter-dependent linear matrix inequalities, and the Lyapunov theory was employed to derive the conditions. Numerical experiments are employed to illustrate the efficacy of the method when considering the 7/ 2 performance criteria.
查看更多>>摘要：For any perfect matching M of a graph G , the forcing number (resp. anti-forcing number) of M is the smallest cardinality of an edge subset S subset of M (resp. S subset of E(G) \ M) such that the graph G - V(S) (resp. G - S) has a unique perfect matching. The forcing spectrum of G is the set of forcing numbers of all perfect matchings of G . Afshani et al. [2] proved that any finite set of positive integers can be the forcing spectrum of a planar bipartite graph. A polyhex is a 2-connected plane bipartite graph whose interior faces are regular hexagons. In this paper, we give the minimum forcing number and anti-forcing number of a polyhex with a 3-divisible perfect matching. Further, we prove that the forcing spectrum of any regular hexagonal polyhex is continuous, i.e. an integer interval, by applying some changes on prolate triangle polyhexes to obtain a sequence of perfect matchings of the graph. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper develops a detailed study of linear and nonlinear stability analyses, for the double diffusive convection problem in a porous medium, when heating is done from below and, salting is done from below as well as from above. The linear analysis is performed using normal mode technique and nonlinear analysis is developed using energy technique. The Chebyshev pseudo-spectral technique is performed to analyze the effect of variable gravity field and throughflow on the behavior of system stability. The results obtained from linear and nonlinear analysis are compared and found that the results are in better agreement for the heated from below and salted from above system however, the comparatively less agreement is obtained for the system when both heating and salting are done from below. The direction of throughflow and gravity field have considerable effect on the stability of system. The behavior of gravity field is invariant for both the type of system heating and salting from below as well as heating from below and salting from above. The solute Rayleigh number stabilizes the system for heating from below and salting from below, however, destabilizes the system for heating from below and salting from above. In the absence of gravity field, a comparatively good agreement between thresholds is seen for Q = 0, however, the agreement is shifted towards positive value of Q or negative value of Q when gravity is found to be present in the system. Thus, effect of gravity field is dominant on the influences of throughflow on the stability of system. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper studies the reachable set estimation for systems with mixed delays and state constraints. Firstly, by constructing an appropriate maximal Lyapunov-Krasovskii functional, combined with the wirtinger-based integral inequality and the extended reciprocally convex combination method, we derive a new criterion about reachable set estimation which reduces the related decision variables without increasing the computational burden. Then, the results are extended to polytopic uncertainties systems and we consider the condition of uncertain differentiable parameters. Three examples are presented to demonstrate the validity of our theorems.
查看更多>>摘要：Let G be any simple undirected graph and let Q(G) be the signless Laplacian matrix of G . The polynomial phi(Q(G), x ) = per(xI - Q(G)) is called the signless Laplacian permanental polynomial of G . The star degree of a graph G is the multiplicity of root 1 of phi(Q(G), x ) . Faria (1985) first considered the star degree of graphs. Based on Faria's results, we further study the features of star degree of graphs, and give a formula to compute the star degree of a graph by a vertex partition of the graph. As applications, we derive the star degree set of n-vertex graphs, and we determine the graphs with extremal star degree. Furthermore, we show that some graphs with given star degree are determined by their signless Laplacian permanental spectra. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：There are numerous financial problems that can be posed as optimal control problems, leading to Hamilton-Jacobi-Bellman or Hamilton-Jacobi-Bellman-Issacs equations. We reformulate these problems as nonlinear PDEs, involving max and/or min terms of the unknown function, and/or its first and second spatial derivatives. We suggest efficient numerical methods for handling the nonlinearity in the PDE through an adaptation of the discrete penalty method Forsyth and Vetzal(2002)[1] that gives rise to tridiagonal penalty matrices. We formulate a penalty-like method for the use with European exercise rights, and extend this to American exercise rights resulting in a double-penalty method. We also use our findings to improve the policy iteration algorithms described in Forsyth and Labahn(2007)[2]. Numerical results are provided showing clear second-order convergence, and where applicable, we prove the convergence of our algorithms. (C) 2022 Published by Elsevier Inc.
NSTL
Elsevier