一类变系数微分方程差分格式的收敛性(英文)  

Convergence of the Difference Scheme for a Class Differential Equations with Variable Coefficients

作　　者：徐琛梅[1] 菅帅[2] 王波[1] 

机构地区：[1]河南大学数学与信息科学学院,河南开封475001 [2]中国科学院数学与系统科学学院,北京100080

出　　处：《应用数学》2012年第3期570-576,共7页Mathematica Applicata

基　　金：Supported by the Natural Science Foundation of the Education Department of Henan Province(2010A100003);the National Natural Science Foundation of China(40805020)

摘　　要：本文首先对一类变系数微分方程建立有限差分格式.然后利用矩阵的特征值和范数理论,讨论该格式解的收敛性和唯一性.通过数值算例,说明该格式既有效又便于模拟.并且文中所用方法还能用于高阶微分方程和某些非线性微分方程问题的研究.In this paper,the finite difference scheme for a class differential equations with variable coefficients is presented. The convergence and uniqueness of the solution for the scheme are proved by means of theories on matrix eigenvalue and norm. The numerical example shows that the scheme is very simple to implement and efficient. This method can be applied to the study of higher-order and some nonlinear differential equations problems.

关 键 词：收敛性 差分格式 变系数微分方程 总体截断误差 

分 类 号：O241.84[理学—计算数学]