一个带约束条件的积分方程的Galerkin法

用Ｇａｌｅｒｋｉｎ法求由多孔直杆扭转问题产生的积分方程的解，证明了相应的变分问题以及离散变分问题都是唯一可解的，由于约束条件的缘故，导出的线性方程组的系数矩阵不是正定的，但本文证明了它的各阶顺序主子式不等于零，从而可用三角分解法或高斯消去法，最后给出了一个数值例子，数值结果是相当满意的。

Galerkin Method for a Restricted Integral Equation

Gaierkin method is used to solve the restricted integral equation arising from elastic torsion of multihole bars.We prove that the corresponding variational problem and discrete variational problem are uniquely solvable.The coefficient matrix of the linear equations is nonpositive definite because of the restrictions,but we prove the leading principal minors of the matrix do not equal zero and the triangular decomposition or Gaussian elimination can be used to the linear equations.A numerical example is given which shows the numerical results are satisfactory.