In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
In this paper, the matrix algebraic equations involved in the optimal control problem of time-invariant linear Ito stochastic systems, named Riccati- Ito equations in the paper, are investigated. The necessary and suf...In this paper, the matrix algebraic equations involved in the optimal control problem of time-invariant linear Ito stochastic systems, named Riccati- Ito equations in the paper, are investigated. The necessary and sufficient condition for the existence of positive definite solutions of the Riccati- Ito equations is obtained and an iterative solution to the Riccati- Ito equations is also given in the paper thus a complete solution to the basic problem of optimal control of time-invariant linear Ito stochastic systems is then obtained. An example is given at the end of the paper to illustrate the application of the result of the paper.展开更多
This is a brief review on the recent book: Duality System in Applied Mechanics and Optimal Control, by Zhong Wan-Xie, published by Kluwer Academic Publishers, 2004. The book represents a significant effort to re-estab...This is a brief review on the recent book: Duality System in Applied Mechanics and Optimal Control, by Zhong Wan-Xie, published by Kluwer Academic Publishers, 2004. The book represents a significant effort to re-establish the historic and deep tie between control and mechanics by striving to connect and integrate concepts, methods, and algorithms in mechanics and control so that a unified framework can be established for both analytical and computational purposes. Clearly, it has demonstrated that the duality system method can be used as a mathematical and systematic foundation to deal with many important concepts and problems in both mechanics and control. This book is not only very useful for research and applications, but also extremely helpful for multidisciplinary curriculum development when students from one field are trying to learning and applying concepts and methods from the other field.展开更多
A scheme for general purposed FDTD visual scientific computing software is introduced in this paper using object-oriented design (OOD) method. By abstracting the parameters of FDTD grids to an individual class and sep...A scheme for general purposed FDTD visual scientific computing software is introduced in this paper using object-oriented design (OOD) method. By abstracting the parameters of FDTD grids to an individual class and separating from the iteration procedure, the visual software can be adapted to more comprehensive computing problems. Real-time gray degree graphic and wave curve of the results can be achieved using DirectX technique. The special difference equation and data structure in dispersive medium are considered, and the peculiarity of parameters in perfectly matched layer are also discussed.展开更多
In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic ...In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.展开更多
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
文摘In this paper, the matrix algebraic equations involved in the optimal control problem of time-invariant linear Ito stochastic systems, named Riccati- Ito equations in the paper, are investigated. The necessary and sufficient condition for the existence of positive definite solutions of the Riccati- Ito equations is obtained and an iterative solution to the Riccati- Ito equations is also given in the paper thus a complete solution to the basic problem of optimal control of time-invariant linear Ito stochastic systems is then obtained. An example is given at the end of the paper to illustrate the application of the result of the paper.
基金Supported by the Outstanding Young Scientist Research Fund from the National Natural Science Foundation of P. R. China (60125310)
文摘This is a brief review on the recent book: Duality System in Applied Mechanics and Optimal Control, by Zhong Wan-Xie, published by Kluwer Academic Publishers, 2004. The book represents a significant effort to re-establish the historic and deep tie between control and mechanics by striving to connect and integrate concepts, methods, and algorithms in mechanics and control so that a unified framework can be established for both analytical and computational purposes. Clearly, it has demonstrated that the duality system method can be used as a mathematical and systematic foundation to deal with many important concepts and problems in both mechanics and control. This book is not only very useful for research and applications, but also extremely helpful for multidisciplinary curriculum development when students from one field are trying to learning and applying concepts and methods from the other field.
基金This project was supported by the National Natural Science Foundation (No. 69831020).
文摘A scheme for general purposed FDTD visual scientific computing software is introduced in this paper using object-oriented design (OOD) method. By abstracting the parameters of FDTD grids to an individual class and separating from the iteration procedure, the visual software can be adapted to more comprehensive computing problems. Real-time gray degree graphic and wave curve of the results can be achieved using DirectX technique. The special difference equation and data structure in dispersive medium are considered, and the peculiarity of parameters in perfectly matched layer are also discussed.
基金The project was supported by the National Natural Science Faundation of China
文摘In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.
