用算子展开法求解 Fredholm 积分方程

SOLUTION OF THE FREDHOLM INTEGRAL EQUATION USING EXPANSION OF OPERATOR

提供了另一种求解积分方程的方法。利用 Hilbert 空间来研究 Fredholm 积分算子,并证明了可利用一组标准正交基将 Fredholn 积分算子展开,从而使积分方程得到简化。应用这一方法给出了一般第二类 Fredholm 积分方程的严格解析解。文中还对具体积分方程进行了求解并与严格解和其它方法所得的解进行了比较,结果吻合得很好。

Another method to solve the integral equation is presented.Fredholm oper-ator is discussed in Hilbert space.Fredholm operator is expanded with orthonormal setsin Hilbert space,so that simplifying the integral equation.Here a integral equation is alsosolved.The results got from the expansion of operator are in good agreement with thoseof the exact solution.