本项目将对奇异积分方程和再生核空间理论及其在科学和工程上的应用作更深一步的研究，涉及到的主要研究内容有奇性核积分方程（包括Chuchy核、Hilbert核和余割核三种）和超奇异积分方程等奇异积分方程的数值求解及数值解的性质，如：收敛性、稳定性和振动性等。 . 拟通过改造传统的再生核函数的解法，并结合现有的方法给出求解以上奇异积分方程的有效算法，从而在再生核空间框架下建立一套理论，并开发具有广泛应用的专业数学软件。因此，本课题的研究不但能够促进奇异积分方程问题处理技术的发展，而且还为许多力学、物理学和工程技术中的实际问题提供强有力的支持。

Theories of singular integral equations and reproducing kernel space and their applications in science and engineering will be further studied. In this project, we will focus on the numerical solutions of integral equations of singular kernel and hypersingular integral equations.Meanwhile,the properties of numerical solutions will be studied, for example, convergence,stability and oscillation.. In this project, we will establish the valid algorithm for solving singular integral equations in the reproducing kernel space by combining with existing methods and improving the traditional methods of reproducing kernel function. Then set up a new theory system in reproducing kernel space and develop the widely useful professional mathematical software. The research of the project not only can promote the development of theories of singular integral equations,but also can provide strong support for the many practical problems in mechanics, physics and engineering technology.