共查询到20条相似文献,搜索用时 168 毫秒
1.
This paper presents an approximate method for solving a class of fractional optimization problems with multiple dependent variables with multi-order fractional derivatives and a group of boundary conditions. The fractional derivatives are in the Caputo sense. In the presented method, first, the given optimization problem is transformed into an equivalent variational equality; then, by applying a special form of polynomial basis functions and approximations, the variational equality is reduced to a simple linear system of algebraic equations. It is demonstrated that the derived linear system has a unique solution. We get an approximate solution for the initial optimization problem by solving the final linear system of equations. The choice of polynomial basis functions provides a method with such flexibility that all initial and boundary conditions of the problem can be easily imposed. We extensively discuss the convergence of the method and, finally, present illustrative test examples to demonstrate the validity and applicability of the new technique. 相似文献
2.
Error estimates for shooting methods in two-point boundary value problems for second-order equations
This paper is concerned with a procedure for estimating the global discretization error arising when a boundary value problem for a system of second order differential equations is solved by the simple shooting method, without transforming the original problem in an equivalent first order problem. Expressions of the global discretization error are derived for both linear and nonlinear boundary value problems, which reduce the error estimation for a boundary value problem to that for an initial value problem of same dimension. The procedure extends to second order equations a technique for global error estimation given elsewhere for first order equations. As a practical result the accuracy of the estimates for a second order problem is increased compared with the estimates for the equivalent first order problem. 相似文献
3.
Lee Yu Y.; Tsai Jason S. H.; Shieh Leang S.; Chen Guanrong 《IMA Journal of Mathematical Control and Information》2005,22(3):266-284
Based on the state-space self-tuning control methodology, aunified method for determining the equivalent linear observer-basedtracker for a stochastic chaotic system with input and statedelays and deterministic disturbances is developed. In thisapproach, an equivalent linear observer is obtained for theconcerned complex system, which may have unknown system parameters,system and measurement noises, and inaccessible system states.More precisely, an equivalent delay-free system is obtainedin the estimating process of the self-tuning control loop, andthen a linear controller and an observer are designed. The proposedmethod significantly simplifies the design and the implementationprocedures of the tracker. 相似文献
4.
武冬 《数学年刊A辑(中文版)》2003,(1)
本文用矩阵的Lozinskii测度的方法,得到了线性常微分方程系统的某些稳定性准则.导出了关于线性系统χ'=A(t)χ稳定性的充要条件.对于A是常数或周期矩阵的情形,我们的结果与从Jordan标准型和Floquet理论得到的经典结论相同. 相似文献
5.
Khaled Omrani 《Numerical Methods for Partial Differential Equations》2004,20(4):527-551
In this article an error bound is derived for a piecewise linear finite element approximation of an enthalpy formulation of the Stefan problem; we have analyzed a semidiscrete Galerkin approximation and completely discrete scheme based on the backward Euler method and a linearized scheme is given and its convergence is also proved. A second‐order error estimates are derived for the Crank‐Nicolson Galerkin method. In the second part, a new class of finite difference schemes is proposed. Our approach is to introduce a new variable and transform the given equation into an equivalent system of equations. Then, we prove that the difference scheme is second order convergent. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 相似文献
6.
本文提出了一种求解线性稳定性理论Orr-Sommerfeld方程的方法.我们首先定义了该方程的Green函数,并将它表达成矩阵形式;然后证明了Green函数的互易性;最后导出了等价于原方程的线性积分方程.该方法适用于两固壁间任意Reynolds数下各种主流速度分布的情况. 相似文献
7.
M.M. Konstantinov P.Hr. Petkov N.D. Christov 《Journal of Computational and Applied Mathematics》1980,6(1):27-35
A method for feedback synthesis of linear control systems with desired linearly equivalent form of the closed loop system matrix is proposed. The method is based on the serial canonical form of linear multivariable systems which is an alternative to the Luenberger canonical form. A stable computational algorithm for finding the serial canonical form using orthogonal similarity transformations is described. The algorithm for synthesis involves a simple recurrent procedure and gives the possibility to achieve any attainable equivalent form of the closed loop system. The results obtained are extended to the synthesis of reduced order state observers. 相似文献
8.
Semiconvergence of nonnegative splittings for singular matrices 总被引:1,自引:0,他引:1
Yongzhong Song 《Numerische Mathematik》2000,85(1):109-127
Summary. In this paper, we discuss semiconvergence of the matrix splitting methods for solving singular linear systems. The concepts
that a splitting of a matrix is regular or nonnegative are generalized and we introduce the terminologies that a splitting
is quasi-regular or quasi-nonnegative. The equivalent conditions for the semiconvergence are proved. Comparison theorem on
convergence factors for two different quasi-nonnegative splittings is presented. As an application, the semiconvergence of
the power method for solving the Markov chain is derived. The monotone convergence of the quasi-nonnegative splittings is
proved. That is, for some initial guess, the iterative sequence generated by the iterative method introduced by a quasi-nonnegative
splitting converges towards a solution of the system from below or from above.
Received August 19, 1997 / Revised version received August 20, 1998 / Published online January 27, 2000 相似文献
9.
We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear system is solved by the preconditioned conjugate gradient (PCG) method with a preconditioner which is shown to be spectrally equivalent to the matrix of the resulting linear system. Numerical tests demonstrating the convergence properties of the scheme and PCG are presented. 相似文献
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12.
模糊Delta算子系统的鲁棒镇定 总被引:1,自引:0,他引:1
研究一类基于Delta算子描述的T-S模糊模型状态反馈镇定设计问题。首先将全局模糊模型按隶属函数划分成若干子空间,并被表示成不确定系统的形式;采用分段Lyapunov函数法,得到鲁棒稳定化控制律存在的充分条件.该条件被进一步等价表示成一组线性矩阵不等式的可解性问题。克服了以往设计法中需要求解一公共正定矩阵P的不足,也无需求解繁琐的Riccati方程。所得结果可将连续和离散模糊系统的有关结论统一到Delta算子框架内。 相似文献
13.
Influence analysis on linear models with random effects 总被引:1,自引:0,他引:1
ZhongXuping WeiBocheng 《高校应用数学学报(英文版)》1999,14(2):169-176
In this paper,a unified diagnostic method for linear models with random effects basedupon the joint likelihood given by Robinson gin 1991) is presented. The case deletion model is e-quivalent to mean shift outlier model,as well as case weights model. From this point of view,several new diagnostic measures,such as Cook disrance,WK diagnostics are derived. Some pre-vious results are improved. Numerical examples illustrate the method is available. 相似文献
14.
周小林 《数学年刊A辑(中文版)》2015,36(3):257-264
用小波伽辽金方法求解多维区域上椭圆型方程齐次Dirichlet问题,构造了近似解空间的两个等价的勒让德多小波基,使得快速求解离散后的线性方程组的多层扩充算法得以实现.数值算例表明该算法是有效的. 相似文献
15.
In this paper, we discuss a class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and fractional derivatives. The necessary optimality conditions are derived and shown that the conditions are sufficient under certain assumptions. Additionally, we design a well-organized algorithm to obtain the numerical solution of the proposed problem by exercising Laguerre polynomials. The key motive associated with the present approach is to convert the concerned fractional optimal control problem to an equivalent standard quadratic programming problem with linear equality constraints. Given examples illustrate the computational technique of the method together with its efficiency and accuracy. Graphical representations are provided to analyze the performance of the state and control variables for distinct prescribed fractions. 相似文献
16.
Equivalent linearization method for the flutter system of an airfoil with multiple nonlinearities 总被引:1,自引:0,他引:1
F.X. Chen Y.M. Chen J.K. Liu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(12):4529-4535
The equivalent linearization method (ELM) was extended to analyze the flutter system of an airfoil with multiple nonlinearities. By replacing the cubic plunging and pitching stiffnesses by equivalent quantities, linearized equations for the nonlinear system were deduced. According to the linearized equations, approximate solutions for limit cycle oscillations (LCOs) were obtained in good agreement with numerical results. The influences of the linear and cubic stiffnesses on LCOs were analyzed in detail. Reducing linear pitching stiffness leads to decreasing of the critical flutter speed. For linear plunging stiffness, the opposite is true. Also, it reveals that the bifurcation could be supercritical or subcritical, which is related to the ratio between the coefficient of cubic pitching stiffness and that of plunging one. 相似文献
17.
《Journal of Applied Mathematics and Mechanics》1998,62(3):479-481
One-dimensional filtration at a rate which decreases hyperbolically, based on the Mints model [1], is considered. The system of model equations with the appropriate initial and boundary conditions is shown to be equivalent to the Goursat problems for hyperbolic equations. This is solved by the Riemann method using a method for finding a Riemann function proposed here. The method gives the well-known results for filtration at a constant rate. The hyperbolic and linear laws of filtration at a decreasing rate are shown to be equivalent under practical conditions of filter use. 相似文献
18.
V. A. Morozov E. M. Mukhamadiev A. B. Nazimov 《Computational Mathematics and Mathematical Physics》2007,47(12):1885-1892
Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived. 相似文献
19.
统计诊断就是对统计推断方法解决问题的全过程进行诊断,而影响分析是统计诊断中十分重要的分支.本文针对半参数广义线性模型,证明了数据删除模型和均值漂移模型的等价性定理,给出了诸如广义Cook距离等诊断统计量并研究了异常点的Score检验统计量,最后通过实例验证了本文给出的诊断方法的有效性。 相似文献