非线性Schrödinger方程的一个线性化紧致差分格式

对非线性Schrödinger方程给出了一个线性化紧致差分格式,运用不动点定理和能量方法证明了格式的唯一可解性,还运用能量方法和数学归纳法,避开困难的先验估计,证明格式在空间方向和时间方向分别具有四阶和二阶精度,数值算例验证了格式的精度和数值稳定性.     

关于一类结构线性方程组

针对从最优化方法、最佳求积公式设计、最小二乘问题求解中导出的一类结构线性代数方程组，首先给出广义奇异值分解分析，然后提出三种求解方案，最后对加权ＱＲ分解的理论性质给出讨论，为进一步研究打下基础     

多圆环柱域上解析函数的边值问题

讨论多圆环柱域上多个复变量的解析函数的Riemann一Hilbert边值问题。通过引入变态的边值问题和对解析函数的Dirichlet边值问题的可解性的证明，给出了解析函数的Riemann－Hilbert边值问题可解的充要条件及解的积分表达式。     

Energy-consistent integration method and its application to hybrid testing

The time-integration algorithm is an indispensable element to determine response of the boundary of the numerical as well as physical parts in a hybrid test. Instability of the time-integration algorithm may directly lead to failure of the test, so stability of an integration algorithm is particularly important for hybrid testing. The explicit algorithms are very popular in hybrid testing, because iteration is not needed. Many unconditionally stable explicit-algorithms have been proposed for hybrid testing. However, the stability analysis approaches used in all these methods are valid only for linear systems. In this paper, a uniform formulation for energy-consistent time integrations, which are unconditionally stable, is proposed for nonlinear systems. The solvability and accuracy are analyzed for typical energy-consistent algorithms. Some numerical examples and the results of a hybrid test are provided to validate the effectiveness of energy-consistent algorithms.