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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

黄晋,吕涛   

  1. 四川大学数学学院,四川大学数学学院 成都,610064 ,成都,610064
  • 出版日期:2004-01-14 发布日期:2004-01-14

黄晋,吕涛. 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[J]. 计算数学, 2004, 26(1): 51-60.

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

  1. Huang Jin Lu Tao (Mathematical College Sichuan University, Chengdu, 610064)
  • Online:2004-01-14 Published:2004-01-14
1.引言借助单层位势理论,平面Dirichlet问题被转化为第一类边界积分方程
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.
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