曲边多角形域上第一类边界积分方程的机械求积算法与分裂外推  

THE MECHANICAL QUADRATURE METHODS AND THEIR SPLITTING EXPRAPOLATIONS FOR FIRST-KIND BOUNDARY INTEGRAL EQUATIONS ON POLYGONAL REGIONS

作　　者：黄晋[1] 吕涛[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《计算数学》2004年第1期51-60,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10171073);教育部博士点基金资助项目.

摘　　要：This paper presents mechanical quadrature methods for solving first-kind boundary integral equations on polygonal regions, which possesses high accuracy O(h0^3)and low computing complexities. Moreover, the multivariate asymptotic expansion of the error with hi^3(i = 1,…,d) power is shown. Using the multi-parameter asymptotic expansion, we not only get a high precisioin approximation solution by means of the splitting extrapolation, but also derive a posteriori estimation.This paper presents mechanical quadrature methods for solving first-kind boundary integral equations on polygonal regions, which possesses high accuracy O(h03) and low computing complexities. Moreover, the multivariate asymptotic expansion of the error with hi3(i - 1,… ,d) power is shown. Using the multi-parameter asymptotic expansion, we not only get a high precisioin approximation solution by means of the splitting extrapolation, but also derive a posteriori estimation.

关 键 词：曲边多角形 第一类边界积分方程 机械求积算法 分裂外推 正弦变换 收敛性 

分 类 号：O175.5[理学—数学]