求解二阶常微分方程的并行块方法  

Parallel block methods for second srder ordinary differential equations

作　　者：束学云[1] 田红炯[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2009年第6期580-587,共8页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金(10671130);上海市科委基础研究项目(06JC14092);上海市教委曙光计划项目(06SG45)

摘　　要：主要研究二阶常微分方程初值问题y″(x)=f(x,y)的数值方法及其数值稳定性.构造了一类适用于并行计算的并行块方法,分析了该类方法的收敛性,得到其最低可达收敛阶.基于线性试验方程y″(x)=-λ2y,提出了并行块方法的P-稳定性定义,获得了二维、三维和四维并行块方法为P-稳定的充分条件.数值例子说明理论结果是正确的.This paper deals with numerical methods for the second - order ordinary differential equations y＂（x） = f（x,y） and their numerical stability property. A class of parallel block methods which are suitable for integrating these equations on parallel computers are proposed. The convergence of such methods is studied and their lowest attainable convergence orders have been obtained. Then we introduce a definition ofP - stability of parallel block methods based on the test equation y＂（x） = - λ2y. Sufficient conditions for the 2 ,3 and 4 - dimensional block methods to be P - stable are established. Numerical experiments are conducted to verify our theoretical results.

关 键 词：二阶常微分方程 并行块方法 收敛阶 P-稳定性 

分 类 号：O241.8[理学—计算数学]