Currently displaying 1 – 20 of 30

Showing per page

Order by Relevance | Title | Year of publication

Drive network to a desired orbit by pinning control

Quanjun WuHua Zhang — 2015

Kybernetika

The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays...

Finite element derivative interpolation recovery technique and superconvergence

Tie Zhu ZhangShu Hua Zhang — 2011

Applications of Mathematics

A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite...

Global superconvergence of finite element methods for parabolic inverse problems

Hossein AzariShu Hua Zhang — 2009

Applications of Mathematics

In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu ZhangShu Hua Zhang — 2015

Applications of Mathematics

We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in d space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order k + 1 in the L 2 -norm if the method uses polynomials of order k . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order k + 1 . Further we consider a residual-based a posteriori...

The gradient superconvergence of the finite volume method for a nonlinear elliptic problem of nonmonotone type

Tie Zhu ZhangShu Hua Zhang — 2015

Applications of Mathematics

We study the superconvergence of the finite volume method for a nonlinear elliptic problem using linear trial functions. Under the condition of C -uniform meshes, we first establish a superclose weak estimate for the bilinear form of the finite volume method. Then, we prove that on the mesh point set S , the gradient approximation possesses the superconvergence: max P S | ( u - ¯ u h ) ( P ) | = O ( h 2 ) | ln h | 3 / 2 , where ¯ denotes the average gradient on elements containing vertex P . Furthermore, by using the interpolation post-processing technique,...

Superconvergence estimates of finite element methods for American options

Qun LinTang LiuShu Hua Zhang — 2009

Applications of Mathematics

In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation...

A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search

Douglas BunkerLixing HanShu Hua Zhang — 2013

Applications of Mathematics

The Alternating Nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we propose to combine it with a periodic enhanced line search strategy. The resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions....

Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media

Shanghui JiaDeli LiTang LiuShu Hua Zhang — 2008

Applications of Mathematics

Asymptotic error expansions in the sense of L -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...

Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations

Shu Hua ZhangTao LinYan Ping LinMing Rao — 2000

Applications of Mathematics

We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be...

Numerical solutions for second-kind Volterra integral equations by Galerkin methods

Shu Hua ZhangYan Ping LinMing Rao — 2000

Applications of Mathematics

In this paper, we study the global convergence for the numerical solutions of nonlinear Volterra integral equations of the second kind by means of Galerkin finite element methods. Global superconvergence properties are discussed by iterated finite element methods and interpolated finite element methods. Local superconvergence and iterative correction schemes are also considered by iterated finite element methods. We improve the corresponding results obtained by collocation methods in the recent...

Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch

Mihua MaHua ZhangJianping CaiJin Zhou — 2013

Kybernetika

This paper is concerned with impulsive practical synchronization in a class of n-dimensional nonautonomous dynamical systems with parameter mismatch. Some simple yet general algebraic synchronization criteria are derived based on the developed practical stability theory on impulsive dynamical systems. A distinctive feature of this work is that the impulsive control strategy is used to make n-dimensional nonautonomous dynamical systems with parameter mismatch achieve practical synchronization, where...

A spatially sixth-order hybrid L 1 -CCD method for solving time fractional Schrödinger equations

Chun-Hua ZhangJun-Wei JinHai-Wei SunQin Sheng — 2021

Applications of Mathematics

We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an L 1 strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid L 1 -CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order 2 - γ in time, where 0 < γ < 1 is the order of the Caputo fractional derivative involved. It...

Page 1 Next

Download Results (CSV)