逆谱问题中偏微分方程数值解的稳定性  

The Stability for the Numerical Solution of a Class of Partial Differential Equations

作　　者：王於平[1] 王薇[2] 马艳婷[1] 

机构地区：[1]南京林业大学理学院应用数学系,江苏南京210037 [2]南京林业大学信息科学技术学院,江苏南京210037

出　　处：《数学的实践与认识》2016年第23期207-215,共9页Mathematics in Practice and Theory

摘　　要：讨论一类偏微分方程数值解的稳定性,这种方程源于Sturm-Liouville算子逆谱问题中变换算子法.证明这类偏微分方程差分格式解的存在性、唯一性、收敛性定理及稳定性定理成立.In this paper we discuss the numerical solution of a class of partial differential equations, which arises from the transformation operator method of inverse spectral problems of Sturm-Liouville operators. Then we will show that the four theorems hold, which are re- spectively existence theorem, uniqueness theorem, convergence theorem and stability theorem for solution of the difference equations of the partial differential equation in the transformation operator method of Sturm-LiouviUe operators.

关 键 词：偏微分方程 数值解 稳定性 逆谱问题 变换算子法 

分 类 号：O241.82[理学—计算数学]