An efficient algorithm for solving Hilbert type singular integral equations of the second kind

作者：Chen Zhong^*; Zhou YongFang

来源：Computers & Mathematics with Applications, 2009, 58(4): 632-640.

DOI：10.1016/j.camwa.2009.01.045

• Hilbert type singular integral equations
• Reproducing kernel space
• Exact solution

A simple and efficient method for solving Hilbert type singular integral equations of the second kind is given. In order to slide over the singularity of the equation, a transform is made. By improving the traditional reproducing kernel method, which requests that the image space of operator is W(2)(1) and that the operator is bounded, the exact solution and the approximate solution of Hilbert type singular integral equations of the second kind are presented. The advantage of the approach lies in the fact that, on one hand, the approximate solution g(n)(x) is continuous. On the other hand. g(n)(x) and g(n)'(x) converge uniformly and rapidly to the exact solution g(x) and its derivatives g'(x) respectively. Numerical experiments show the efficiency of our method.

• 出版日期2009-8
• 单位哈尔滨工业大学; 黑龙江科技大学