某第二类Fredholm积分方程的一种数值解法

我们考虑第二类 Fredholm积分方程的快速数值解法 .本文假设核函数除在 x=t处带有弱奇性外 ,是解析的 [1] .我们利用分片多项式插值逼近核函数 ,由此得到近似的系数矩阵 A.设 n为积分节点的个数 ,k2为每个小区域的插值节点数 ,我们证明矩阵 A的计算和矩阵 -向量相乘 Ax各需要 O( nk)次运算 ,存贮 A需要占用 O( nk)内存 .最后我们对算法的稳定性进行讨论并给出数值结果

An O(nk) Solver for Fredholm Equations of the Second Kind with Weakly Singular Kernels

A new fast solver for Fredholm integral equations of the second kind is considered.It is assumed that the kernel functions are analytic except that they are weakly singular when x=t.To obtain approximate coeffcient matrix ,one can use piec wise polynomial interpolation to approximate the kernel functions.Let n be the number of quadrature points,k 2 be the number of interpolating knots at each subdomain.It is proved that the construction of and the matrix vector multipliation x require O(nk) operations respectively.The storage of is also O(nk).Finally,the stability of the alogrithm is discussed and numerical results are given to illustrate the stability and efficiency of our algorithms.