解平面弹性力学问题的边界积分方程的机械求积方法及其外推  

MECHANICAL QUADRATURE METHODS AND THEIR EXTRAPOLATIONS FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF PLANE ELASTICITY 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：《计算数学》2001年第4期491-502,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助项目.

摘　　要：By means of the quadrature rules of computing singular periodic functions, mechanical quadrature methods for solving boundary integral equations of plane elasticty problems are presented, which possess high accuracies and low computing complexities. Moreover, the asymptotic expansions with the odd powers of the errors are shown, so that we not only can improve the accuracy order of the approximations by Richardson extrapolation but also can estimate the errors of the approximations by a posteriori error estimations.By means of the quadrature rules of computing singular periodic functions, mechanical quadrature methods for solving boundary integral equations of plane elasticty problems are presented, which possess high accuracies and low computing complexities. Moreover, the asymptotic expansions with the odd powers of the errors are shown, so that we not only can improve the accuracy order of the approximations by Richardson extrapolation but also can estimate the errors of the approximations by a posteriori error estimations.

关 键 词：边界积分方程 平面弹性问题 机械求积方法 数值方法 积分算子 位移边值问题 奇异积分方程组 

分 类 号：O343[理学—固体力学]