【摘要】 借助位势理论，平面双调和方程的Ｄｉｒｉｃｈｌｅｔ问题被转化为第一类边界积分方程组．本文使用新型的反常积分的求积公式构造出解此类边界积分方程的机械求积方法，证明了该方法具有Ｏ（ｈ３）阶精度和误差的ｈ３幂渐近展开，故借助Ｒｉｃｈａｒｄｓｏｎ外推还能提高精度阶．更多还原

【Abstract】 By means of potential theory, the biharmonic Dirichlet problem can be trans- fered to a boundary inteqral equation system of the first kind. This paper presents a quadra- ture method for solving boundary integral equation system of biharmonic Dirichlet problem, which possesses accuracy 0(h3). Moreover, the asymptotic expansion with h3 power of the error is shown, so we can improve the accuracy order of the approximations by Richardson extrapolation.更多还原