Optimal superconvergent one step quadratic spline collocation methods

We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena. AMS subject classification (2000)  65N35, 65N22     

拟矩形剖分上的样条空间的维数

矩形剖分~(记为$\Delta_{QR}$)~是指在矩形剖分~(记为$\Delta_{R}$)的基础上进行局部修改后得到的剖分,通常包括T-剖分~(记为$\Delta_{T}$)~和L-剖分~(记为$\Delta_{L}$).本文利用光滑余因子协调方法讨论了该剖分上的二元样条空间$S^\mu_k(\Delta_{QR})$的维数.在满足一定约束条件下, 得到了仅依赖于样条空间的次数,光滑度和剖分拓扑结构的显式维数公式.     

内陷在C_(60)中的氢原子的性质

在短程球形势阱的模型下 ,运用线性变分法并采用B 样条作为展开基函数计算了内陷于C60 几何中心的氢原子能谱和波函数 ,并计算了势阱深度对能谱的影响 ,详细讨论了内陷氢原子表现出的一系列特殊性质 ,从而对低维半导体材料性能的研究提供了有效的数据 ;同时这一工作也表明 ,用线性变分法结合B 样条函数在处理这类问题时是非常有效的。     

Quasistrategies in an abstract guidance control problem

We consider an abstract guidance control problem with elements of uncertainty, where the control procedures are identified with set-valued quasistrategies. The goal of the control consists in the guidance to the objective set under phase constraints.We construct the solvability set by the method of program iterations which is well known in the theory of differential games. We prove that the limit of the iterative procedure has the sense of the set of positional absorption (the stable bridge) introduced by N. N. Krasovskii. This limit coincides with the solvability set in the class of quasistrategies.     

A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon

A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three‐points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved for a scheme based on the product two‐point Gaussian quadrature by establishing a relation with an underdetermined orthogonal spline collocation scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

我国人口时间序列的变系数预测模型

根据1952-2005年我国人口总量和GDP总量数据,建立变系数模型.采用逐步回归的方法来选择显著滞后变量子集,推导出系数函数的样条估计表达式,最后运用Bootstrap思想,进行点预测和区间预测。运算结果表明:对于该组数据,变系数模型能较理想地描述数据之间的内在结构,且具有较少的预测误差.     

A class of optimal iterative methods of inverting a linear bounded operator

A family of higher-order iterative methods for inverting a linear bounded operator in a Banach space is presented. This family depending on two integer parameters can be considered as hyperpower methods of [1]. A convergence Theorem is proved and an optimal class with respect to the efficiency index is determined . Several error bounds are derived and compared with those in the literature.     

Mixed convection boundary layer flow of non-Newtonian fluids along vertical wavy plates

Mixed convection boundary layer flows of non-Newtonian fluids over the wavy surfaces are studied by the coordinate transformation and the cubic spline collocation numerical method. The effects of the wavy geometry, the buoyancy parameter and the generalized Prandtl number for pseudoplastic fluids, Newtonian fluids and dilatant fluids on the skin-friction coefficient, local and mean Nusselt numbers have been graphically studied. Results show that both higher generalized Prandtl numbers and buoyancy parameters are seen to enhance the influence of wavy surfaces on the local Nusselt number, irrespective of whether the fluids are Newtonian fluids or non-Newtonian fluids. Moreover, the irregular surfaces have higher total heat flux than that of corresponding flats plate for any fluid.     

非理想压杆稳定分析的样条函数法

采用样条函数构造的位移模式，出了非理想压杆稳定极限承载力及稳定平衡全过程的样条函数分析法。本方法可以考虑任意实际初始缺陷和材料弹塑性加卸载效应的影响。计算表明，本方法精度高，速度快。