Approximate solution to an integral equation with fixed singularity for a cruciform crack

A novel method for determining an approximate solution to an integral equation with fixed singularity is presented. This integral equation is encountered in solving a cruciform crack. On the basis of Taylor’s series for the unknown function, the integral equation can be transformed to a system of linear equations for the unknown and its derivatives when neglecting a sufficiently small quantity. Moreover, the nnth-order approximation obtained is exact for a solution of a polynomial of degree less than or equal to nn. The proposed method is simple, fast, and can be performed by symbolic computation using any personal computer. A test example is given to indicate the efficiency of the method. This method is also applicable to a variety of integral equations.