Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation

Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations are applied to the nonlinear advection equa-tion. The results show that the approach is effective for the exact analytical solu-tion and the algorithm has higher precision than other existing algorithms in nu-merical computation for the nonlinear advection equation.

Algebraic dynamics solution and algebraic dynamics algorithm of Burgers equations

Algebraic dynamics solution and algebraic dynamics algorithm of nonlinear partial differential evolution equations in the functional space are applied to Burgers equation. The results indicate that the approach is effective for analytical solutions to Burgers equation, and the algorithm for numerical solutions of Burgers equation is more stable, with higher precision than other existing finite difference algo-rithms.

模拟退火算法的改进及其应用

模拟退火算法是随机优化近似算法.本文首先介绍其物理背景和一般形式,然后通过对算法增加记忆和返回两个功能以及在算法之后链接一个局部搜索过程,改善了算法性能,接着将改进算法应用于解旅游商问题,最后对该算法作简要的性能评论.

求全局最优解的新算法

利用局部极大值点与动力系统的稳定奇点的对应性,计算代数方程的根、无约束极大值点、有约束极大值点、非线性规划解、及最小二乘解.我们采用了常微分方程数值解的Euler算法及网格初始点的循序迭代算法,并以具体的例子和程序说明创立的方法具有通用性,同时考虑了一些存在的问题以便在理论和算法上作进一步的改进.

轴对称任意梯度圆筒的弹性动力学解

基于轴对称平面应变问题的运动方程及弹性梯度材料的应力和位移关系,通过将圆筒分层使材料性质离散为分段常数函数,同时在时域内应用有限差分格式,求得了材料性质沿径向梯度变化的圆筒弹性动力学解。本文解不仅适合任意梯度的弹性圆筒,而且容易满足多种形式的初始条件和边界条件。通过对材料性质沿径向为连续函数分布和分段函数分布的梯度圆筒数值分析,并与已有文献结果比较,得出本文解与已有文献的解吻合较好,验证了本文解的正确性和有效性。对材料性质为分段函数的三层组合圆筒分析发现,中间功能梯度层的指数分布因子对圆筒的径向位移和应力随时间变化都会产生显著影响。

一类积分Altman型映象不动点定理及应用

本文在非阿基米德概率度量空间中研究积分Altman型映象不动点的存在性,利用概率度量空间映象对相容条件建立了积分Altman型映象的公共不动点定理;作为应用讨论了起源于动态规划的一类泛函方程组公共解的存在与唯一性,从而改进和推广了一些已知结果。

半空间热弹性问题的新解法

本文给出一个半空间热弹性问题的新解法。这个解法的主要特点是使用了Ｈａｎｓｅｎ通解，由边界条件将半空间热弹性问题化为求解线性代数方程组的问题。这个解法还可应用于其它的一些弹性力学问题。