科研之友
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摘要
This paper presents quadrature formulas for Cauchy singular integrals. The asymptotic expansions of the errors with the power h(2 mu) (mu = 1, ... , m) are obtained by Euler-Maclaurin expansions. In the first part of this work, we derive formulas for One-dimension Cauchy singular integral and their corresponding Euler-Maclaurin expansion on the basis of the midpoint rule and Sidi-Israeli's quadrature formulas for the boundary integral equations with weak singularities. In the second part of this work, we propose the quadrature formulas for the Two-dimension singular integral on the basis of quadrature formulas for the One-dimension Cauchy singular integral. For calculating singular integrals the algorithms are very simple and straightforward, without calculation any derivative value of function, the accuracy order of the algorithms is very high.
