一类不连续发展型集值方程的广义单调迭代法  

General monotone iterative method for a class of discontinuous evolution set-valued equation

作　　者：田岩[1] 周磊[2] 

机构地区：[1]华中科技大学图像识别与人工智能研究所图像信息处理与智能控制教育部重点实验室 [2]华中科技大学数学系

出　　处：《华中科技大学学报（自然科学版）》2002年第6期105-107,共3页Journal of Huazhong University of Science and Technology(Natural Science Edition)

摘　　要：利用序理论及广义单调迭代法研究了一类非线性不连续发展型集值方程 ,引入序理论给出其迭代格式 ,在空间中通过一个正凸锥定义一个序结构 ,并给出此问题的迭代格式 (即广义单调迭代法 ) ,应用序理论得到连续问题迭代解的收敛结果 .还给出一个合理的离散格式及其数值解法 ,在局部上半利普希茨条件下 。A class of nonlinear discontinuous set valued evolution equation was discussed by using order theory and the general monotone iterative method. An order structure was defined via a positive convex cone in a linear space, and an iterative scheme (i.e. general monotone iterative method) for the nonlinear discontinuous problems was given. Applying order theory, the convergence of iterative solution for continuous problem was obtained. A rational discrete form and the numerical method for the discrete equation were given. Under the locally upper Lipschitz condition, the convergence of solution, the convergence of solution set was studied.

关 键 词：不连续发展型 集值方程 广义单调迭代法 收敛性 

分 类 号：O175.29[理学—数学]