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应用科学学报 ›› 1985, Vol. 3 ›› Issue (4): 306-312.

• 论文 • 上一篇    下一篇

第一种Fredholm积分方程的数值解法

李明忠   

  1. 复旦大学
  • 收稿日期:1982-07-24 修回日期:1985-04-28 出版日期:1985-12-31 发布日期:1985-12-31

THE NUMERICAL SOLUTION OF THE FIRST-KIND FREDHOLM INTEGRAL EQUATIONS

LI MINGZHONQ   

  1. Fudan University
  • Received:1982-07-24 Revised:1985-04-28 Online:1985-12-31 Published:1985-12-31

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167

被引次数

3

摘要： 在本文中,研究形如
∫-11 k(t,s)y(s) ds=f(t),t∈[-1,1]
的第一种Fredholm积分方程的数值解法,其中f(t)在[-1,1]上连续,核k(t,s)一般是弱奇性的,它可表为
k(t,s)=h(t,s)m(t,s),
这里h(t,s)具有形如h(t,s)=|t-s|α,α>-1的弱奇性,m(t,s)是连续函数.本文应用Lagrange多项式内插法,构造了一个近似解序列,并证明了它的收敛性.

Abstract: In this poper, we study the numerical solution of the first-kind Fredholm integral equation
∫-11 k(t,s)y(s)ds=f(t),t∈[-1,1]
where f(t) is continuous and k(t, s) may be weakly singular. The kernel k(t, s) is assumed to be expressed as k(t, s)=h(t, s)m(t, s), where h(t, s) is of a standard form for example h(t, s)=|t-s|α, α>-1, and m(t, s) is continuous. By using Lagrange polynomial interpolation, a sequence of the approximate solution is established and the convergence is proved.