预估-校正方法的绝对稳定性讨论  

THE ABSOLUTE STABILITY PROPERTIES OF PREDICTOR-CORRECTOR METHODS

作　　者：刘冬兵[1] 杨大地[2] 

机构地区：[1]攀枝花学院计算机学院,四川攀枝花617000 [2]重庆大学数理学院,重庆400044

出　　处：《计算数学》2011年第3期321-327,共7页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10671132)资助项目

摘　　要：预估-校正方法,即PECE方法,常被用于求解常微分方程的初值问题.而一般文献中常只讨论了单个线性多步法公式的稳定性问题,很少涉及由一个显式公式和一个隐式公式组合而成的PECE方法的稳定性.本文应用根轨迹法和对分法讨论了常用的PECE方法的稳定性,求出了一些常用PECE方法的组合公式的绝对稳定区间和绝对稳定区域,并用数值试验对结果进行了验证.The PECE methods, so called predictor-corrector methods, are often used for solving initial value problems of ordinary differential equations. The research on stability of linear multistep methods at present mainly concerned with single formula but rarely with the PECE method composed of an explicit formula and an implicit formula. We discussed the stability of PECE methods by means of the bisection method and the root locus method in this paper, reported the absolute stability interval and absolute stability region of some often used PECE methods. Then the results are verified through the numerical experiment.

关 键 词：线性多步方法 预估-校正方法 稳定性 

分 类 号：O241.81[理学—计算数学]