一类二维对偶积分方程的解及其应用

A Class of Two-Dimensional Dual Integral Equations and Its Application

二维对偶积分方程的理论与方法,在数学上尚未建立,因而完全的分析解不可能得到,从而使一些力学、物理与工程问题无法求解.利用双重展开和边界配置方法,得到了在数学和物理学上有着广泛应用的一类二维对偶积分方程的解答.把二维对偶积分方程化简成无限代数方程组,此方法的精确度取决于计算点的配置(即所谓边界配置).通过对固体力学中某些复杂的初值_边值问题的应用说明此是方法有效的.

Because exact analytic solution was not available,the double expansion and boundary collocation were used to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics. The integral equations by this procedure were reduced to infinite algebraic equations. The accuracy of the solution lies in the boundary collocation technique. The application of which for some complicated initial-boundary value problems in solid mechanics indicates the method is powerful.