共查询到20条相似文献,搜索用时 46 毫秒
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l introductionThe vortex system is a system of POint voids, and a model Of incompressible inviscidnow inspired by the idea of an almOSt POtence flOW. The voracity in the now is concentratedin N-vortices (i. e., POints at which the vortloty field is singUlar) [4]. An ideal incompressible now can be approximated by the motion Of a ~ system which is not only a usefulheuristic tool in the analysis of the general propelles of solutionS Of Euler equations, but also auseful stachg POint for th… 相似文献
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Camil I. Aponte Román 《代数通讯》2017,45(4):1793-1807
We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of a?ne group schemes and are in correspondence with graded Hopf algebras. Graded group varieties take the place of infinitesimal group schemes. We generalize the result that connected graded bialgebras are graded Hopf algebra to our setting and we describe the algebra structure of graded group varieties. We relate these new objects to the classical ones providing a new and broader framework for the study of graded Hopf algebras and a?ne group schemes. 相似文献
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We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations by introducing a new notion of consistency. Our results are robust and general - they improve and extend earlier results by Krylov, Barles, and Jakobsen. We apply our general results to various schemes including Crank-Nicholson type finite difference schemes, splitting methods, and the classical approximation by piecewise constant controls. In the first two cases our results are new, and in the last two cases the results are obtained by a new method which we develop here.
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Bruno Casella Gareth Roberts Osnat Stramer 《Methodology and Computing in Applied Probability》2011,13(4):835-854
A broad class of implicit or partially implicit time discretizations for the Langevin diffusion are considered and used as
proposals for the Metropolis–Hastings algorithm. Ergodic properties of our proposed schemes are studied. We show that introducing
implicitness in the discretization leads to a process that often inherits the convergence rate of the continuous time process.
These contrast with the behavior of the naive or Euler–Maruyama discretization, which can behave badly even in simple cases.
We also show that our proposed chains, when used as proposals for the Metropolis–Hastings algorithm, preserve geometric ergodicity
of their implicit Langevin schemes and thus behave better than the local linearization of the Langevin diffusion. We illustrate
the behavior of our proposed schemes with examples. Our results are described in detail in one dimension only, although extensions
to higher dimensions are also described and illustrated. 相似文献
6.
We introduce a new Euler-type scheme and its iterative algorithm for solving weakly coupled forward-backward stochastic differential equations (FBSDEs). Although the schemes share some common features with the ones proposed by C. Bender and J. Zhang [Ann. Appl. Probab., 2008, 18: 143–177], less computational work is needed for our method. For both our schemes and the ones proposed by Bender and Zhang, we rigorously obtain first-order error estimates, which improve the half-order error estimates of Bender and Zhang. Moreover, numerical tests are given to demonstrate the first-order accuracy of the schemes. 相似文献
7.
Summary. We propose globally convergent
iteration schemes for updating the eigenvalues of a symmetric
matrix after a rank-1 modification. Such calculations are the
core of the divide-and-conquer technique for the symmetric
tridiagonal eigenvalue problem. We prove the superlinear
convergence right from the start of our schemes which allows us
to improve the complexity bounds of [3]. The effectiveness of
our algorithms is confirmed by numerical results which are
reported and discussed.
Received September 22, 1993 相似文献
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In this paper we develop a novel approach to construct non-stationary subdivision schemes with a tension control parameter which can reproduce functions in a finite-dimensional subspace of exponential polynomials. The construction process is mainly implemented by solving linear systems for primal and dual subdivision schemes respectively, which are based on different parameterizations. We give the theoretical basis for the existence, uniqueness, and refinement rules of schemes proposed in this paper. The convergence and smoothness of the schemes are analyzed as well. Moreover, conics reproducing schemes are analyzed based on our theory, and a new idea that the tensor parameter ωk of the schemes can be adjusted for conics generation is proposed. 相似文献
9.
Jian Ren 《Advances in Computational Mathematics》2009,31(1-3):267-281
Digital watermarking has been widely used in digital rights management and copyright protection. In this paper, new cryptographic watermark schemes are proposed. Compare to the existing watermarking techniques, our proposed watermark schemes combine both security and efficiency that none of the existing schemes can do. We first develop an algorithm to randomly generate the watermark indices based on the discrete logarithm problem (DLP) and the Fermat’s little theorem. Then we embed watermark signal into the host image in both time domain and frequency domain at the indices. Our security analysis and simulation demonstrate that our proposed schemes can achieve excellent transparency and robustness under the major security attacks and common signal degradations. The novel approaches provided in this paper are ideal for general purpose commercial digital media copyright protection. 相似文献
10.
Families of parameter dependent univariate and bivariate subdivision schemes are presented in this paper. These families are new variants of the Lane-Riesenfeld algorithm. So the subdivision algorithms consist of both refining and smoothing steps. In refining step, we use the quartic B-spline based subdivision schemes. In smoothing step, we average the adjacent points. The bivariate schemes are the non-tensor product version of our univariate schemes. Moreover, for odd and even number of smoothing steps, we get the primal and dual schemes respectively. Higher regularity of the schemes can be achieved by increasing the number of smoothing steps. These schemes can be nicely generalized to contain local shape parameters that allow the user to adjust locally the shape of the limit curve/surface. 相似文献
11.
In this paper, some two-grid finite element schemes are constructed for solving the nonlinear Schrödinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy. 相似文献
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Yidu Yang 《计算数学(英文版)》2009,27(6):748-763
This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou (Math. Comput., 70 (2001), pp.17-25) to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is reduced to that on a much coarser mesh together with the solution of a linear algebraic system on the fine mesh. The resulting solution still maintains an asymptotically optimal accuracy. Comparing with the two-grid discretization scheme of the conforming finite elements, the main advantages of our new schemes are twofold when the mesh size is small enough. First, the lower bounds of the exact eigenvalues in our two-grid discretization schemes can be obtained. Second, the first eigenvalue given by the new schemes has much better accuracy than that obtained by solving the eigenvalue problems on the fine mesh directly. 相似文献
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In this paper two adaptive sliding mode controls for synchronizing the state trajectories of the Genesio–Tesi system with unknown parameters and external disturbance are proposed. A switching surface is introduced and based on this switching surface, two adaptive sliding mode control schemes are presented to guarantee the occurrence of the sliding motion. The stability and robustness of the two proposed schemes are proved using Lyapunov stability theory. The effectiveness of our introduced schemes is provided by numerical simulations. 相似文献
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Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper. We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points, which greatly improves the efficiency of numerical computations. The optimal error estimates are derived by using some traditional approaches and techniques. Lastly, some numerical results are provided to verify our theoretical analysis. 相似文献
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V. I. Paasonen 《Numerical Analysis and Applications》2018,11(1):60-72
In this paper, various difference schemes with oblique stencils, i.e., schemes using different space grids at different time levels, are studied. Such schemes may be useful in solving boundary value problems with moving boundaries, regular grids of a non-standard structure (for example, triangular or cellular ones), and adaptive methods. To study the stability of finite difference schemes with oblique stencils, we analyze the first differential approximation and dispersion. We study stability conditions as constraints on the geometric locations of stencil elements with respect to characteristics of the equation. We compare our results with a geometric interpretation of the stability of some classical schemes. The paper also presents generalized oblique schemes for a quasilinear equation of transport and the results of numerical experiments with these schemes. 相似文献
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Shlomi Dolev Evangelos Kranakis Danny Krizanc 《Journal of Algorithms in Cognition, Informatics and Logic》1999,30(2):379
This paper presents scheduling of packet transmission schemes, calledbaked-potatoschemes, which are used to avoid simultaneous arrival of packets at a switch. We present scheduling schemes for any capacity of links and switches. The schemes are evaluated by the maximal length of time between two successive schedulings of a processor. For the case of a single-capacity link and switch, our scheme is proved optimal by presenting a matching lower bound. Our baked-potato scheme does not assume any prior knowledge on the source–destination demands and can be used for sending control packets and broadcasting. 相似文献
17.
Using the forms of Newton iterative function, the iterative function of Newton's method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this paper and show that their convergence order is at least quadratic. At last we employ our methods to solve some non-linear equations and compare them with Newton's method and Halley's method. Numerical results show that our iteration schemes are convergent if we choose two suitable parametric functions λ(x) and μ(x). Therefore, our iteration schemes are feasible and effective. 相似文献
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In this paper, three numerical schemes with high accuracy for the coupled Schrodinger equations are studied. The conserwtive properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable. 相似文献
20.
Yulong Xing & Chi-Wang Shu 《数学研究》2014,47(3):221-249
In this paper, we survey our recent work on designing high order positivity-preserving
well-balanced finite difference and finite volume
WENO (weighted essentially non-oscillatory) schemes, and discontinuous Galerkin finite element
schemes for solving the shallow water equations with a non-flat bottom topography.
These schemes are genuinely high order accurate
in smooth regions for general solutions, are essentially non-oscillatory
for general solutions with discontinuities, and at the same time
they preserve exactly the water at rest or the more general moving water steady state solutions.
A simple positivity-preserving limiter, valid under suitable CFL condition,
has been introduced in one dimension and reformulated to two
dimensions with triangular meshes, and we prove that the resulting schemes guarantee
the positivity of the water depth. 相似文献