摘要
研究Cauchy核中多复变微分方程自回归线性解初值问题,为物理控制和生物医学演化等数学模型的构建提供数学基础。特别在高温冷却下的温度场有限元分析控制中具有重要的控制应用价值,采用非线性微分方程解分析的方法,通过对方程的多个逼近特征解进行分析,提取出所有解的特征,从而求解稳定解,此方法在多解相关性强的情况下具有较好的效果。在两个状态时滞向量的Cauchy核中求解多复变微分方程泛函,得到自回归线性解初值的最小正特征带状的连接权,根据Cauchy核中多复变微分方程泛函,得到Cauchy核最优解和Cauchy核最优边界,通过证明得到Cauchy核中多复变微分方程的自回归线性初值是连续收敛和渐进稳定的,且在闭环控制性能曲面上至少有一个稳定解。分析结果有利于提高高温冷却下的温度场有限元分析控制性能。
The linear self-regression initial solution value problem of multi complex variables differential equation in Cauchy kernel is researched, as it provides the mathematical basis for physical control and biomedical evolution control. The analysis of the method for the solution of nonlinear differential equation. In the two state time delay vector of Cauchy nucleus in solving a complex differential equations obtained from functional, connection weight minimum positive characteristic banded linear regression of solutions to the initial value, according to the Cauchy kernel in the complex differential equation functional, Cauchy kernel optimal solution and Cauchy kernel optimal boundary are obtained, the evidence obtained from regression linear initial value Cauchy the nuclear of several complex variables differential equation is continuous convergence and asymptotic stability of the closed-loop control performance, and there is at least one stable solution on the control performance surface. Results are beneficial to improve the high temperature cooling of the finite element analysis of the temperature control performance.
出处
《科技通报》
北大核心
2015年第2期7-9,共3页
Bulletin of Science and Technology
关键词
CAUCHY核
微分方程
自回归
初值问题
Cauchy kernel
differential equation
autoregression
initial value problem
