关于D-K法并行圆盘迭代

改进了Durand-Kerner方法并行圆盘迭代的收敛性条件，所用证明方法相当简明。     

代数Riccati方程数值解的一种牛顿迭代法

代数Riccati方程在优化控制理论中具有十分重要的作用.结合了二次方程的牛顿迭代法与Lya-punov方程的自由参数轮转方向迭代法,提出了一种求代数Riccati方程数值解的一种新方法,并给出了算法的收敛性证明.最后,给出了具体的数值算例.     

一类广义混合变分不等式组解的强收敛定理

研究了Banach空间中一类广义混合变分不等式组问题,引进了一种新的迭代算法,研究了由迭代算法生成的序列的收敛性,并得到了这类变分不等式组解的强收敛定理,从而推广和改进了相关文献的一些工作.     

解Lyapunov 矩阵方程的改进的梯度迭代算法

In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples.     

热学教学中应用迭代法的实例

迭代法是计算数学中常用的一种求各类方程的近似解的计算方法。在解代数方程、超越方程、微分方程和积分方程时,使用迭代法常常可以比较快捷方便地得到方程足够精确的近似解。本文通过热学课程教学中的一些实例,介绍了应用迭代法时所遇到的诸如“初始值的选取”、“迭代公式的选择”、“迭代结果呈现出的发散趋势”等方面的相关知识。     

Solution of stress intensity factors of multiple cracks in plane elasticity with eigen COD formulation of boundary integral equation

The concept of eigen crack opening displacement (COD) can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an it...     

用迭代函数系统构造分形图形

讨论了一类具有自相似分形图形生成的数学方法——迭代函数系统，并举例说明图形的生成。     

Variational iteration method for solving Fokker-Planck equation

In this paper variational iteration method is implemented to solve linear and nonlinear Fokker-Planck equations, and some similar equations. To illustrate the simplicity and reliability of the method some examples are provided and comparisons are made between the variational iteration method and the Adomian decomposition method. Comparison shows that variational iteration method is more effective and convenient to use and overcomes the difficulty arising in calculating Adomian polynomials. Also, this method can successfully be applied to a large class of problems.     

An efficient method for solving Emden–Fowler equations

In this paper, He's variational iteration method (VIM) is applied to solve the Emden–Fowler type equations in the second-order ordinary differential equations (ODEs). In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The Lagrange multipliers in the functionals can be identified optimally via variational theory. This technique provides a sequence of functions which convergence to the exact solutions of the Emden–Fowler equations. Comparison with the exact solutions and the solutions by the Adomian decomposition method (ADM) show efficiency of VIM in solving equations with singularity.     

线性方程组的解法在计算机上的实现

阐述通过EXCEL解决线性方程组的迭代方法,并在结果的基础上对Jacobi和Gauss-Sidel两种迭代方法进行比较。