平面双调和问题的第一类边界积分方程的高精度求积方法与外推  

QUADRATURE METHODS WITH HIGH ACCURACY AND THEIR EXTRAPOLATION FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF PLANE BIHARMONIC PROBLEMS

作　　者：吕涛[1] 黄晋[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《应用数学学报》2001年第3期321-332,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金资助项目.

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．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.

关 键 词：双调和方程 边界积分方程 求积方法 DIRICHLET问题 RICHARDSON外推 位势理论 精度阶 边界元法 

分 类 号：O411.1[理学—理论物理] O175.5[理学—物理]