解析与数值的意义及所描述的世界  

Analytical and Numerical Significance and the Description of the World

作　　者：张本祥[1] 孙博文[2] 

机构地区：[1]黑龙江大学哲学学院,黑龙江哈尔滨150080 [2]哈尔滨理工大学计算中心,黑龙江哈尔滨150080

出　　处：《系统科学学报》2013年第4期18-21,共4页Chinese Journal of Systems Science

基　　金：黑龙江省教育厅人文社会科学项目(11552206);教育部人文社会科学研究一般项(10YJA720040)

摘　　要：基本科学规律一般指动力学规律即状态时间变化的微观规律,呈现为"边界条件+动力学方程"形式。动力学方程是潜无限意义下的微分方程,少数简单情况下有解析解,初等连续函数形式的解析解描述的是一个确定性、连续性的世界;多数情况下没有解析解,那是一个不确定性和非线性放大机制并存的世界;潜无限动力学方程不能完全描述的是实无限的连续性世界。在运动学层面,无论有无解析解也无论存不存在动力学方程,都可以用数值方法研究动力学现象的运动学行为,数值解描述的是有限性、确定性、离散性、历史性的世界。Basic scientific laws generally refer to dynamical laws that are micro laws of state changes, appearing as ＂boundary condition plus dynamics equation＂. Dynamics equations are differential equations in the sense of potential infinite. They have analytical solutions in the form of elementary continuous func- tions only in a few simple cases to represent a world with certainty and continuity, while in most cases there is no analytical solution for the world where uncertainty coexists with nonlinear amplification mecha- nism. Potential infinite dynamics equation couldn＇ t completely represent the continuity world. In the aspect of kinematics, numerical method is always effective regardless of of the real infinite analytical solution or dynamics equation. Numerical solutions represent a finite, certain, discrete and historic world.

关 键 词：动力学 解析解 数值解 意义 世界 

分 类 号：N941[自然科学总论—系统科学]