A Family of Integrable Rational Semi-Discrete Systems and Its Reduction

Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.     

抛物型积分微分方程的非协调$H^{1}$-Galerkin混合有限元方法

H^1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type. By use of the typical characteristic of the elements, we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method, but without LBB stability condition.     

非线性半离散森林系统的可控性

讨论森林发展系统的一类非线性林龄面积结构的半离散模型,利用矩阵的秩判据证明了森林半离散系统的可控性.     

直接配置法求解连续铸钢过程中的最优控制问题

利用描述连续铸钢过程二冷区喷水控制下钢的热传导的半离散化模型 ,我们构造一包含温度梯度约束的最优控制问题 .针对此最优控制问题 ,采用直接配置法进行数值求解 ,得出相应的近似最优控制 .     

Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem are trivial, in the sense that all of them are shown to reduce to the first conserved density of the AKNS hierarchy in the continuum limit. We derive new and nontrivial infinitely many conservation laws for the sdAKNS hierarchy, and also the explicit combinatorial relations between the known conservation laws and our new ones. By performing a uniform continuum limit, the new conservation laws of the sdAKNS system are then matched with their counterparts of the continuous AKNS system.     

EQ 1 rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations

EQ rot 1 nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2 ) one order higher than its interpolation error O(h), the superclose results of order O(h2 ) in broken H1 -norm are obtained. At the same time, the global superconvergence in broken H1 -norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4 ) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ rot 1 element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.     

一类非线性四阶双曲方程扩展的混合元方法的超收敛分析

对一类非线性四阶双曲方程利用双线性元Q_(1)及Nedelec's元建立一个扩展的协调混合元逼近格式.首先证明了逼近解的存在唯一性.其次,基于上述两个单元的高精度结果,给出了插值和投影之间的误差估计,再利用对时间t的导数转移技巧和插值后处理技术,在半离散和全离散格式下分别导出了原始变量u和中间变量v=-△u在H~1模及中间变量q=▽u,σ=-▽(△u)在(L~2)~2模意义下单独利用插值和投影所无法得到的具有O(h~2)和O(h~2+τ~2)阶的超收敛结果.最后通过数值算例,表明逼近格式是行之有效的.这里,h和τ分别表示空间剖分参数及时间步长.     

Sobolev方程一个新的H~1-Galerkin混合有限元分析

研究了Sobolev方程的H~1-Galerkin混合有限元方法.利用不完全双二次元Q_2~-和一阶BDFM元,建立了一个新的混合元模式,通过Bramble-Hilbert引理,证明了单元对应的插值算子具有的高精度结果.进一步,对于半离散和向后欧拉全离散格式,分别导出了原始变量u在H~1-模和中间变量p在H(div)-模意义下的超逼近性质.     

The semi-discrete method for solving high-dimension wave equation

The article gives a semi-discrete method for solving high-dimension wave equation. By the method, high-dimension wave equation is converted by means of discretization into I-D wave equation system which is well-posed. The convergence of the semidiscrete method is given. The numerical calculating results show that the speed of convergence is high.     

大型纵向加筋截断锥壳稳定性的半离散分析

如何计算大型纵向加筋截断锥壳的稳定问题，尚未见到有关报导。本文在沿纵向和环向分别采用Ｈｅｒｍｉｔｅ插值和三角级数插值的基础上，建立了几何非线性带筋环单元，进而导出了半离散分析法，并经过实例检验了它的正确与可靠。这样，本文为建立各类工程结构的半离散单元提出了一种新的途径。