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

✍ Scribed by Bao-Qing Tang; Xian-Fang Li

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 218 KB
• Volume: 21
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2007.12.022

✦ Synopsis

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 nth-order approximation obtained is exact for a solution of a polynomial of degree less than or equal to n. 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.