中文摘要：

利用Legendre多项式的定义和性质，给出Legendre多项式微分算子矩阵，得到任意阶弱奇异积分的近似求积公式，并将原方程转换为代数方程．收敛性分析说明该方法是收敛的，数值算例验证了该方法的有效性和理论分析的正确性．

英文摘要：

One derivative operational matrix of Legendre polynomials is given by using the definition of Legendre potyno- mials and some properties. And an approximate formula which solves solution of arbitrary order weakly singular integral is also obtained and the original equation is transformed into algebraic equation Convergence analysis shows that the method is convergent. Finally, numerical example is provided to verify the validity of the method and the correctness of the theoretical analysis.