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1.
A new approach based on a global state space form is introduced for solving trajectory optimization problems with state inequality constraints via indirect methods. The use of minimal coordinates on a boundary arc of the state constraint eliminates severe problems, which occur for standard methods and are due to the appearance of differential-algebraic boundary-value problems. Together with a hybrid approach and a careful treatment of some interior-point conditions, we obtain an efficient and reliable solution method.  相似文献   

2.
This paper aims to develop a novel numerical approach on the basis of B-spline collocation method to approximate the solution of one-dimensional and two-dimensional nonlinear stochastic quadratic integral equations. The proposed approach is based on the hybrid of collocation method, cubic B-spline, and bi-cubic B-spline interpolation and Itô approximation. Using this method, the problem solving turns into a nonlinear system solution of equations that is solved by a suitable numerical method. Also, the convergence analysis of this numerical approach has been discussed. In the end, examples are given to test the accuracy and the implementation of the method. The results are compared with the results obtained by other methods to verify that this method is accurate and efficient.  相似文献   

3.
交通流灰色RBF网络非线性组合预测方法   总被引:1,自引:1,他引:0  
针对智能交通系统的开发,提出一种基于灰色GM(1,1)模型和RBF网络非线性组合的短时交通流预测方法.该方法采用三层结构的RBF网络将两种单一预测方法(灰色GM(1,1)模型和RBF网络)进行了非线性组合.利用实测数据对组合方法进行了仿真实验,结果表明:非线性组合模型的预测准确性高于单独的RBF网络预测的准确性;组合模型发挥了两种单一方法各自的优势,是短时交通流预测的有效方法.  相似文献   

4.
In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007  相似文献   

5.
Summary. Hybrid methods for the solution of systems of linear equations consist of a first phase where some information about the associated coefficient matrix is acquired, and a second phase in which a polynomial iteration designed with respect to this information is used. Most of the hybrid algorithms proposed recently for the solution of nonsymmetric systems rely on the direct use of eigenvalue estimates constructed by the Arnoldi process in Phase I. We will show the limitations of this approach and propose an alternative, also based on the Arnoldi process, which approximates the field of values of the coefficient matrix and of its inverse in the Krylov subspace. We also report on numerical experiments comparing the resulting new method with other hybrid algorithms. Received May 27, 1993 / Revised version received November 14, 1994  相似文献   

6.
In this study, we use two direct algebraic methods to solve a fourth-order dispersive cubic-quintic nonlinear Schrödinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law. By using complex envelope ansatz method, we first obtain a new dark soliton and bright soliton, which may approach nonzero when the time variable approaches infinity. Then a series of analytical exact solutions are constructed by means of F-expansion method. These solutions include solitary wave solutions of the bell shape, solitary wave solutions of the kink shape, and periodic wave solutions of Jacobian elliptic function.  相似文献   

7.
An approach for combining Arbitrary–Lagrangian–Eulerian (ALE) moving-mesh and level-set interface tracking methods is presented that allows the two methods to be used in different spatial regions and coupled across the region boundaries. The coupling allows interface shapes to be convected from the ALE method to the level-set method and vice-versa across the ALE/level-set boundary. The motivation for this is to allow high-order ALE methods to represent interface motion in regions where there is no topology change, and the level-set function to be used in regions where topology change occurs. The coupling method is based on the characteristic directions of information propagation and can be implemented in any geometrical configuration. In addition, an iterative method for the hybrid formulation has been developed that can be combined with pre-existing solution methods. Tests of a propagating interface in a uniform flow show that the hybrid approach provides accuracy equivalent to what one is able to obtain with either of the methods individually.  相似文献   

8.
Interior-point methods are among the most efficient approaches for solving large-scale nonlinear programming problems. At the core of these methods, highly ill-conditioned symmetric saddle-point problems have to be solved. We present combinatorial methods to preprocess these matrices in order to establish more favorable numerical properties for the subsequent factorization. Our approach is based on symmetric weighted matchings and is used in a sparse direct LDL T factorization method where the pivoting is restricted to static supernode data structures. In addition, we will dynamically expand the supernode data structure in cases where additional fill-in helps to select better numerical pivot elements. This technique can be seen as an alternative to the more traditional threshold pivoting techniques. We demonstrate the competitiveness of this approach within an interior-point method on a large set of test problems from the CUTE and COPS sets, as well as large optimal control problems based on partial differential equations. The largest nonlinear optimization problem solved has more than 12 million variables and 6 million constraints.  相似文献   

9.
In this paper we propose a hybrid between direct and indirect boundary integral methods to solve a transmission problem for the Helmholtz equation in Lipschitz and smooth domains. We present an exhaustive abstract study of the numerical approximation of the resulting system of boundary integral equations by means of Galerkin methods. Some particular examples of convergent schemes in the smooth case in two dimensions are given. Finally, we extend the results to a thermal scattering problem in a half plane with several obstacles and provide numerical results that illustrate the accuracy of our methods depending on the regularity of the interface.  相似文献   

10.
Recently, Herrera presented a general theory of domain decomposition methods (DDM). This article is part of a line of research devoted to its further development and applications. According to it, DDM are classified into direct and indirect, which in turn can be subdivided into overlapping and nonoverlapping. Some articles dealing with general aspects of the theory and with indirect (Trefftz–Herrera) methods have been published. In the present article, a very general direct‐overlapping method, which subsumes Schwarz methods, is introduced. Also, this direct‐overlapping method is quite suitable for parallel implementation. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 495–517, 2001  相似文献   

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