摘要
把数学规划引进加权残值法,给出微分方程问题的一种新的近似解法,即数学规划加权残值法(简记为MP-MWR)。如果在问题的定义域V中存在解w(x),那么该解被任意两个满足定解条件的函数w_u(x)和w_l(x)夹住,即若有RW_u≥0≥Rw_l,恒有w_u≥w≥w_l,在域V内这里,R是残余算子。应用最优化技术,还能够得到满足上述不等式的minW_u和maxW_l。MP-MWR相对于有限元法而言,可减少计算机内存单元的需求量。本文给出了数字例题。
This paper presents a new method of treating differential equations. In this method Mathematical Programming is introduced into the Method of Weighted Resridual (MWR). It is known as Methematical Programming MWR (abbreviated as MP-MWR). If solution w(x) exists in the defining domain V of problems, it is bracked by any two functions w_u(x) and w_l(x). They satisfy the definite conditions that if Rw_u≧o≧Rw_l, thenw_u≧w≧w_l in V Where R is the residual operator.By using the method of optimzation, we can also get min w_uand max w_lto satisfy the above inequality. The advatage of MP-MWP is that the storage cell requirements in computer can be decreased as compared with the Finite Element Method. At the end of the paper the numerical examples are given.
出处
《天津大学学报》
EI
CAS
CSCD
1991年第4期31-36,共6页
Journal of Tianjin University(Science and Technology)
关键词
数学规划
加权残值法
单调法
mathematical programming, method of weighted residual, constrained random direction search method
