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应用科学学报 ›› 1998, Vol. 16 ›› Issue (3): 285-290.

• 论文 • 上一篇    下一篇

Fredholm第一类积分方程数值解的可靠性

李春芳1, 赵葆常2   

  1. 1. 上海大学;
    2. 中国科学院西安光机所
  • 收稿日期:1996-12-02 修回日期:1997-06-06 出版日期:1998-09-30 发布日期:1998-09-30
  • 作者简介:李春芳:副教授,博士,上海大学理学院物理系,上海 201800

Reliability of the Numerical Solution to the Fredholm Integral Equation of the First Kind

LI CHUNFANG1, ZHAO BAOCHANG2   

  1. 1. Shanghai University, Shanghai 201800;
    2. Xi'an Institute of Optics and Precision Mechanics, Xi'an 710068
  • Received:1996-12-02 Revised:1997-06-06 Online:1998-09-30 Published:1998-09-30

PDF

114

被引次数

5

摘要： 讨论了一个Fredholm第一类积分方程数值解的可靠性问题.对于Fabry-Perot干涉反演光谱学中的第一类积分方程,当△e=2/x,△x=2/e,且等距取样点数为一个适当的奇数时,虽然采用最简单的矩形求积公式可离散得一个稳定的线性方程组,但是该方程组的解却不是原积分方程的解,换句话说,该稳定的数值解是不可靠的.

关键词: 数值解的可靠性, Fredholm第一类积分方程, 干涉反演光谱学

Abstract: This paper discusses the reliability of the numerical solution to a Fredholm integral equation of the first kind. Although a stable system of linear equations can be obtained from the integral equation of the first kind in the Fabry-Perot inverse interfe rence spectroscopy, by using the simplest rectangle formula, in the case △e=2/x, △x=2/e and the number of equally-spaced sampling points being a suitable odd one, its solution is not the solution to the original integral equation. That is to say, the stable numerical solution is not reliable.

Key words: reliability of numerical solution, Fredholm integral equation of the first kind, inverse interference spectroscopy