某第二类Fredholm积分方程的一种数值解法  

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

作　　者：吴静[1] 林福荣[1] 

机构地区：[1]汕头大学数学系,汕头515063

出　　处：《汕头大学学报（自然科学版）》2003年第1期11-18,共8页Journal of Shantou University：Natural Science Edition

摘　　要：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 .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.

关 键 词：FREDHOLM积分方程 插值多项式 快速矩阵向量乘法 广义极小剩余法 

分 类 号：O241.8[理学—计算数学]