改进的新型显式Numerov算法应用于含有扰动振子的二阶微分方程的计算  

Application of Improved New Explicit Numerov Method to Calculation of Second Order Differential Equations Containing Perturbation Oscillator

作　　者：张超[1] 李明[1] 

机构地区：[1]河北北方学院理学院,河北张家口075000

出　　处：《河北北方学院学报（自然科学版）》2011年第3期7-10,共4页Journal of Hebei North University:Natural Science Edition

摘　　要：首先介绍了Numerov算法及应用方向,接下来引出由Scheifele提出的基于G函数的Numerov算法,说明此算法的特点与缺陷.之后,讨论了在Scheifele的G函数之后,由Franco对其作出改进,所提出的函数的构造过程与重要性质,并分析了Franco的基于函数的Numerov算法的先进性与缺陷.在此基础上,通过对经典Numerov算法和现有的四阶显式Numerov算法的整合与拓展,利用扰动振子,提出一种改进的新型显式Numerov算法.经过数值计算检验,表明新的算法具有较小的扰动性,较高的精度,较好的稳定性,较之前的算法是一种更加行之有效的方法.This paper first introduces the Numerov method and its application direction.Then it raises the Numerov method based on G function and proposed by Scheifele,and its characteristics and defects.The construction process and important properties of the -function proposed by Franco after Scheifele＇s G-function are discussed,And the advanced nature and defects of Franco＇s Numerov method based on the -function are analyzed.Based on the classical Numerov method and integration and development of existing fourth-order explicit Numerov method,and using perturbation oscillator,an improved perturbation oscillator explicit Numerov method is proposed.The numerical test shows that the new method has the smaller perturbation,higher accuracy and better stability.Compared with the previous algorithm it is a more effective method.

关 键 词：Numerov算法 扰动振子 主局部截断误差 数值 扰动参数 

分 类 号：O175.23[理学—数学]