Numerical solution of Volterra–Fredholm integral equations based on εε-SVR method

In this paper, we try to study the numerical methods for solving integral equations from a new perspective—machine learning method. By means of the idea of kernel εε-support vector regression machine (εε-SVR), we construct an optimization modeling for a class of Volterra–Fredholm integral equations and propose a novel numerical method for solving them. The proposed method has a certain versatility and can be used to solve some other kinds of integral equations. In order to verify the effectiveness of the proposed method, we perform a series of comparative experiments with six specific Volterra–Fredholm integral equations and a method proposed in Wang et al. (2014). Experimental results show that the proposed method has a good approximation property.