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iterative method for Solving a Problem with Mixed Boundary Conditions for Biharmonic Equation

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Advances in Applied Mathematics and Mechanics 2009年第5期1卷 683-698页

作者： Dang Quang A Le Tung Son Institute of Information Technology 18 Hoang Quoc Viet Cau giayHanoiVietnam Pedagogic College Thai Nguyen UniversityVietnam

The solution of boundary value problems(BVP)for fourth order differential equations by their reduction to BVP for second order equations,with the aim to use the available efficient algorithms for the latter ones,attracts attention from many *** this paper,using the technique developed by the authors in recent works we construct iterative method for a problem with complicated mixed boundary conditions for biharmonic equation which is originated from nanofluidic *** convergence rate of the method is proved and some numerical experiments are performed for testing its dependence on a parameter appearing in boundary conditions and on the position of the point where a transmission of boundary conditions occurs.

关键词： iterative method biharmonic equation mixed boundary conditions

iterative method on Well Bore Boundary in Numerical Modeling of Variably Saturated Flow

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Transactions of Tianjin University 2012年第2期18卷 104-111页

作者：王俊黄岁樑 Chiu on Ng College of Environmental Science and Engineering Nankai University Department of Fundamental Subject Tianjin Institute of Urban Construction Department of Mechanical Engineering The University of Hong Kong

An iterative method was developed for incorporating the well bore boundary into the finite difference model of water flow in variably saturated porous media. Six cases were presented involving groundwater pumping or injection to demonstrate the advantages of the iterative method over the traditional method. For the iterative method, the total flux gradually approached the well discharge and the flux profile was non-uniform. And the iterative method took into account the variation of well bore water table. Compared to the traditional method, the iterative method can simulate the variably saturated flow caused by pumping or injection more realistically.

关键词： iterative method variably saturated flow well bore boundary flux profile

iterative method for Constructing Complete Complementary Sequences with Lengths of 2^mN

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Tsinghua Science and Technology 2005年第5期10卷 605-609页

作者：张超韩承镐廖懿婷林孝康羽鸟光俊 Department of Electronic Engineering Tsinghua University Beijing 100084 China Department of System and Information Engineering University of Tsukuba Ibaraki 305-0006 Japan National Institute of Informatics Chiyoda Tokyo 101-8430 Japan

Complete complementary sequences are widely used in spectrum spread communications because of their ideal correlation functions. A previous method generates complete complementary sequences with lengths of N^nN （n,N ∈ Z^＋）. This paper presents a new iterative method to construct complete complementary sequences with lengths of 2^mN （m,N ∈ Z^＋）. The analysis proves that this method can produce many sequence sets that do not appear in sequence sets generated by the former method, especially shorter sequence sets. The result will certainly increase the application of complete complementary sequences in communication engineering and related fields.

关键词： complete complementary sequences iterative method code division multiple access (CDMA)

An iterative method for Optimal Feedback Control and Generalized HJB Equation

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IEEE/CAA Journal of Automatica Sinica 2018年第5期5卷 999-1006页

作者： Xuesong Chen Xin Chen the school of applied mathematics guangdong university of technologyGuangzhou 510006China the school of electromechanical engineering guangdong university of technologyGuangzhou 510006China

Abstract--In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman （GHJB） equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems. Index Terms--Generalized Hamilton-Jacobi-Bellman （HJB） equation, iterative method, nonlinear dynamic system, optimal control.

关键词： Generalized Hamilton-Jacobi-Bellman(HJB) equation iterative method nonlinear dynamic system optimal control

Modified iterative method for augmented system

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Applied Mathematics and Mechanics(English Edition) 2014年第4期35卷 503-514页

作者：邵新慧季翠沈海龙李长军 Department of Mathematics Northeastern University

The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.

关键词： successive overrelaxation-like (SOR-like) method modified SOR-like (MSOR-like) method augmented system iterative method

A Spectral iterative method for the Computation of Effective Properties of Elastically Inhomogeneous Polycrystals

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Communications in Computational Physics 2012年第3期11卷 726-738页

作者： Saswata Bhattacharyya Tae Wook Heo Kunok Chang Long-Qing Chen Department of Materials Science and Engineering The Pennsylvania State UniversityUniversity ParkPA 16802USA

We report an efficient phase field formalism to compute the stress distribution in polycrystalline materials with arbitrary elastic inhomogeneity and *** dependence of elastic stiffness tensor on grain orientation is taken into account,and the elastic equilibrium equation is solved using a spectral iterative perturbation *** discuss its applications to computing residual stress distribution in systems containing arbitrarily shaped cavities and cracks(with zero elastic modulus)and to determining the effective elastic properties of polycrystals and multilayered composites.

关键词： Elasticity spectral method iterative method

Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing iterative method

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Computer Modeling in Engineering & Sciences 2023年第5期135卷 1111-1130页

作者： Chein-Shan Liu Essam REl-Zahar Yung-Wei Chen Center of Excellence for Ocean Engineering Center of Excellence for the OceansTaiwan Ocean UniversityKeelung202301Taiwan Department of Mathematics College of Sciences and Humanities in Al-KharjPrince Sattam bin Abdulaziz UniversityAlkharj11942Saudi Arabia Department of Basic Engineering Science Faculty of EngineeringMenofia UniversityShebin El-Kom32511Egypt Department of Marine Engineering Taiwan Ocean UniversityKeelung202301Taiwan

How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear *** decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear *** the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly *** each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very *** numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).

关键词： Nonlinear algebraic equations novel splitting-linearizing technique iterative method maximal projection optimal splitting parameter

A SIGNIFICANT IMPROVEMENT ON NEWTON’S iterative method

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Applied Mathematics and Mechanics(English Edition) 1999年第8期20卷 103-106页

作者：吴新元 Department of Mathematics Nanjing University Nanjing 210093 China

For solving nonlinear and transcendental equation f(x)=0 , a singnificant improvement on Newton's method is proposed in this paper. New “Newton Like” methods are founded on the basis of Liapunov's methods of dynamic system. These new methods preserve quadratic convergence and computational efficiency of Newton's method, and remove the monotoneity condition imposed on f(x):f′(x)≠0 .

关键词： nonlinear equation transcendental equation dynamic system iterative method Newton's method numerical analysis

A Fourth-Order Convergent iterative method by Means of Thiele's Continued Fraction for Root-Finding Problem

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Journal of Mathematical Research with Applications 2019年第1期39卷 10-22页

作者： Shengfeng LI Institute of Applied Mathematics Bengbu University

In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele’s continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.

关键词： non-linear equation Thiele’s continued fraction Viscovatov algorithm iterative method order of convergence