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1.
Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when
viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms
whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential
equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration
process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using
the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order
algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions”
defined by nonvanishing Lie brackets. 相似文献
2.
I. J. Lozada J. C. Osorio D. V. Griffiths M. Cerrolaza 《Numerical Methods for Partial Differential Equations》2006,22(2):296-316
The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
3.
关新民 《新疆大学学报(理工版)》2002,19(1):95-99
介绍了采用MATLAB V5.2提供的模糊逻辑工具箱来设计研究电孤纺电极调节系统中的模糊--PD控制器,讨论了在SIMULINK环境下模糊-PD控制器的参数自调速原理、结构、建立模糊控制规则库和模糊推论方法,并给出仿真结果与结论。 相似文献
4.
François Ledrappier Mark Pollicott 《Bulletin of the Brazilian Mathematical Society》2005,36(2):143-176
In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚp) on ℚp × ℚp and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually
associated to GL(2,ℚp)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension
of the geodesic flow. 相似文献
5.
6.
Guido Consonni Piero Veronese Eduardo Gutirrez-Pea 《Journal of multivariate analysis》2004,88(2):335-364
Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations. 相似文献
7.
Keith Jonathan M. Kroese Dirk P. Bryant Darryn 《Methodology and Computing in Applied Probability》2004,6(1):29-53
A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis–Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis. 相似文献
8.
XIE Fu-Ding Xiao-Shan LIU Feng 《理论物理通讯》2004,42(11)
Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained. 相似文献
9.
Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising. 相似文献
10.
V. Afraimovich A. Babin S.-N. Chow 《Transactions of the American Mathematical Society》1996,348(12):5031-5063
The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.