This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of max...This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of maximal and minimal solutions are obtained.展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
Iterative feedback tuning is an attractive method for industry as it is a model free approach using experiments conducted on the plant to tune controller parameters. Classically Gauss-Newton iterative methods are used...Iterative feedback tuning is an attractive method for industry as it is a model free approach using experiments conducted on the plant to tune controller parameters. Classically Gauss-Newton iterative methods are used in IFT to update the controller parameters in the negative gradient direction of a specified design criterion function. Levenburg-Marquardt and Trust-Region strategies offer attractive advantages to Gauss-Newton in many applications,these alternative methods are given and results from simulation presented. A discussion on the differences between line search methods and Trust-Region methods is given showing the Trust-Region search direction is more flexible. Step size selection is often the limiting factor and it is found that with unknown step size values and initial controller parameters the Trust-Region is the best selection,where as if overshoot is a concern Levenburg-Marquardt is a good choice.Gauss-Newton method provides quick convergence and a fast response time however it shows more dependence on the step size.展开更多
In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal...In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.展开更多
In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results([9,11,13]). Second, we also give the convergent theorem of...In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results([9,11,13]). Second, we also give the convergent theorem of the GMPOR method, which generalizes the corresponding result of [9]. Finally, we provide the real interval such that the generalized extrapolated Jacobi iterative method and the generalized SOR methods simultaneously converge, one of the main results in [1] is extended.展开更多
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with...Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.展开更多
基金Supported by NNSF-China (No.10071043)the YNSF of Shandong Province (No.Y2000A06)
文摘This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of maximal and minimal solutions are obtained.
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
文摘Iterative feedback tuning is an attractive method for industry as it is a model free approach using experiments conducted on the plant to tune controller parameters. Classically Gauss-Newton iterative methods are used in IFT to update the controller parameters in the negative gradient direction of a specified design criterion function. Levenburg-Marquardt and Trust-Region strategies offer attractive advantages to Gauss-Newton in many applications,these alternative methods are given and results from simulation presented. A discussion on the differences between line search methods and Trust-Region methods is given showing the Trust-Region search direction is more flexible. Step size selection is often the limiting factor and it is found that with unknown step size values and initial controller parameters the Trust-Region is the best selection,where as if overshoot is a concern Levenburg-Marquardt is a good choice.Gauss-Newton method provides quick convergence and a fast response time however it shows more dependence on the step size.
基金Research supported by the NSF of Shandong Province (Y2004A01) the foundation of SDAI(XN040101).
文摘In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.
文摘In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results([9,11,13]). Second, we also give the convergent theorem of the GMPOR method, which generalizes the corresponding result of [9]. Finally, we provide the real interval such that the generalized extrapolated Jacobi iterative method and the generalized SOR methods simultaneously converge, one of the main results in [1] is extended.
基金the National Natural Science Foundation of China(No.10671060)the Doctoral Fund of Ministry of Education of China granted[2003]0532006
文摘Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
