Approximate Solutions of a Hypersingular Boundary Integral Equation

In the paper, a reproducing kernel method of solving hypersingular integral equations (HSIE) with cosecant kernel is proposed. Difficulties lie in its singular term of solving HSIE. In order to remove singular term, hypersingular term with square cosecant kernel is transformed into singular term with Hilbert kernel. Subsequently, by making a equivalent transformation singular term with Hilbert kernel is removed. It´s advantages the series representation of solution is obtained in a reproducing kernel Hilbert space. On the other hand, the representation of reproducing kernel becomes simple by improving the definition of traditional inner product and requirements for image space of operators are weakened comparing with traditional reproducing kernel method. The final numerical experiments illustrate the method is efficient.