第一类Fredholm积分方程的解析解

The Analytic Solution of Fredholm Integral Equation of The First Kind

在 W(1/2)[a,b]空间中,利用再生核给出第一类 Fredholm 积分方程解析解的表述式.当方程右端以离散形式给出时,可直接构造数值解,而且当节点无限加密时,数值解一致收敛于解析解,其误差按空间的范数单调下降.

In this paper,we discuss how to solve Fredholm integral equation of the first kind in space W_2~1[a,b] and with the help of reproducing kernel, we have obtained the expression of the analytic solution.When the right side of the equation is given in the discrete form,we can directly construct the numerical solution which approaches uniformly to the analytic solution as the knots are increased infinitely,and whose error decreases monotonous- ly in norm of space.