第一种Fredholm积分方程的数值解法

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.

THE NUMERICAL SOLUTION OF THE FIRST-KIND FREDHOLM INTEGRAL EQUATIONS

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.